GRK 1132:  Stochastics and Real World Models

• Subject Area: Mathematics
• Term: from 2006 to 2014
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 772176

• Final Report Year: 2015

Final Report Abstract

The central general idea for the research programme of the IRTG was to further develop specific areas of stochastic analysis that have made enormous progress in recent years. This was to be done aiming at new applications in mathematical physics and economics. A major goal of this IRTG was to provide a generation of young scientists from China and Germany with a high-level truly inter-disciplinary education. The graduates were to gain a strong background in all three areas (stochastics, mathematical physics and mathematical economics) and a lot of experience in communicating and exchanging ideas with colleagues not only in their own area of specialization. The emphasis on a strong background in all fields is not only important to be able to identify the relevant research questions in the considered field of application, where state-of-the-art mathematical techniques can be usefully applied, but also to be able to communicate the importance of the results and of such an interdisciplinary approach to the research community in the applied fields. During the nine years of its existence the IRTG has achieved substantial progress in all aspects of the above overall goals, documented through a substantial number of publications by the IRTG’s altogether 78 graduates in journals, that are among the top ones in the respective fields. During the the nine years, in particular, during the second period the research within the IRTG which was structured in three clusters: (I) Stochastic Analysis, (II) Models in Mathematical Physics and (III) Models in Finance and Economics, focused on the following topics: Dirichlet forms and Markov processes as well as their relations to stochastic partial differential equations; functional inequalities and heat kernel estimates; free and quantum probability, in particular random matrix theory and determinantal point processes; continuum configuration spaces and interacting particles systems; dynamical properties of complex networks; and open quantum systems and quantum information theory. A combining element for all these subfields was the methodological approach dominated by new methods, recent developments and latest results from stochastics, in particular stochastic analysis.

Publications

• Lagrangian Singularities of steady two-dimensional flow, Geophys. Astrophys. Fluid. Dyn. 99 (2005), 61–75
  W. Pauls, T. Matsumoto
  
• An Axiomatic Approach to Composite Solutions, IMW Working Paper 385 (2006)
  D. Dimitrov, C.-J. Haake
  
• Nature of complex singularities for the 2D Euler equation, Physica D 219 (2006), 40–59
  W. Pauls, T. Matsumoto, U. Frisch and J. Bec
  
• Stable Coalition Structures in Simple Games with Veto Control, IMW Working Paper 384 and CentER Discussion Paper 2006–114 (2006)
  B. Ciftci, D. Dimitrov
  
• The representations of two types of functionals on L∞ (Ω, F) and L∞ (Ω, F, P ), Science in China Series A: Mathematics 49(10) (2006), 1376–1382
  Yo. Song, J.-A. Yan
  
• (Quasi-)Regular Dirichlet forms for particle systems on Polish spaces, Frontiers of Mathematics in China 4 (2007), 583–598
  G.-Q. Lan, F.-Y. Wang
  
• A Borel transform method for locating singularities of Taylor and Fourier series, J. Stat. Phys. 127 (2007), 1095–1119
  W. Pauls, U. Frisch
  
• Coverage Problem of Wireless Sensor Networks, Lecture Notes in Computer Science 4381, Discrete Geometry, Combinatorics and Graph Theory (2007), 88–100
  G.-L. Lan, Z.-M. Ma, S.-Y. Sun
  
• Equilibrium Glauber dynamics of continuous particle systems as a scaling limit of Kawasaki dynamics, Random Oper. Stoch. Equ. 15(2) (2007), 105–126
  D. Finkelshtein, Y. Kondratiev, E. Lytvynov
  
• Even regular factors of regular graphs and number of cut edges, Southeast Asian Bulletin of Mathematics 31 (2007), 1019–1026
  L. Xiao, Y. Liu
  
• Geoantineutrino spectrum and slow nuclear burning on the boundary of the liquid and solid phases of the Earth’s core, J. Geophys. Res. 112 (2007), B09203
  V. D. Rusov, V. N. Pavlovich, V. N. Vaschenko, V. A. Tarasov, T. N. Zelentsova, V. N. Bolshakov, D. A. Litvinov, S. I. Kosenko, O. A. Byegunova
  
• Point interaction Hamiltonians in bounded domains, J. Math. Phys. 48 (2007), 082108
  P. Blanchard, R. Figari, A. Mantile
  
• Procedural Group Identification, Mathematical Social Sciences 54(2) (2007), 137–146
  D. Dimitrov, S.-C. Sung, Y. Xu
  
• Quantumness of bipartite states in terms of conditional entropies, J. Phys. A: Math. Theor. 40 (2007), 11361-11371
  N. Li, S. Luo and Z. Zhang
  
• Some classes of Markov processes on configuration spaces and their applications, PhD thesis (2007)
  N. Ohlerich
  
• The Sharp Threshold for Asymptotic Connectivity in Wireless Networks, Dynamics of Continuous, Discrete and Impulsive Systems 14(S7) (2007), 160–163
  S.-Y. Sun
  
• Total versus quantum correlations in quantum states, Phys. Rev. A 76 (2007), 032327
  N. Li and S. Luo
  
• A note on equilibrium Glauber and Kawasaki dynamics for fermion point processes, Methods Funct. Anal. Topol. 14 (2008), 67–80
  E. Lytvynov, N. Ohlerich
  
• A note on strong limit theorems for arbitrary stochastic sequences, Statistics & Probability Letters 78(14) (2008), 2018–2023
  W. Yang and X. Yang
  
• A Note on the Paradox of Smaller Coalitions, Social Choice and Welfare 30(4) (2008), 571–579
  D. Dimitrov, C.-J. Haake
  
• A randomized distributed algorithm for total scheduling problem, The 7th International Symposium on Operations Research and Its Applications (ISORA) (2008), 311–316
  L. Xiao, G. Yan, W. Ren, Xu Li
  
• Classical states versus separable states, Phys. Rev. A 78 (2008), 024303
  N. Li and S. Luo
  
• Criteria for ergodicity of Lévy type operators in dimension one, Stochastic Processes and their Applications 118 (2008), 1909–1928
  J. Wang
  
• Dimension-free Harnack inequality and applications for SPDE under variational framework, Oberwolfach Reports no. 50 (2008), 2852–2855
  W. Liu
  
• Genesis of d’Alembert’s paradox and analytical elaboration of the drag problem, Physica D 237 (2008), 1878–1886
  G. Grimberg, W. Pauls, U. Frisch
  
• Harnack inequality and strong Feller property for stochastic fast diffusion equations, J. Math. Anal. Appl. 342 (2008), 651–662
  W. Liu, F.-Y. Wang
  
• Hyperviscosity, Galerkin truncation and bottlenecks, Phys. Rev. Lett. 101 (2008), 144501
  U. Frisch, S. Kurien, R. Pandit, W. Pauls, S. S. Ray, A. Wirth, J.-Zh. Zhu
  
• Induced Subgraph in Random Regular Graph, Journal of Systems Science and Complexity 21(4) (2008), 645–650
  L. Xiao, G. Yan, Y. Wu, W. Ren
  
• Invariance Principle for Diffusions in Random Environment, Condensed Matter Physics 11(2) (2008), 275–282
  S. Struckmeier
  
• On two-component contact model in continuum with one independent component, Methods Funct. Anal. Topology 14(3) (2008), 209–228
  D. Filonenko, D. Finkelshtein, Y. Kondratiev
  
• Quasi sure q-variation of a type of continuous two-parameter Gaussian process, SFB 701 Preprint 08132 (2008)
  K. He
  
• Selection-Mutation Balance Models with Epistatic Selection, Condensed Matter Physics 11(2) (2008), 283–291
  Y. Kondratiev, T. Kuna, N. Ohlerich
  
• Stable Governments and the Semistrict Core, Games and Economic Behavior 62(2) (2008), 460–475
  D. Dimitrov, C.-J. Haake
  
• Week superadditivity of skew information, J. Phys. A: Math. Theor. 41 (2008), 135301
  L. Cai, N. Li and S. Luo
  
• An overview of representation theorems for static risc measures, Science in China Ser. A: Mathematics 52(7) (2009), 1412–1422
  Yo. Song, J.-A. Yan
  
• Asymptotic behavior of some stochastic evolutions in continuum, PhD thesis (2009)
  S. Struckmeier
  
• CAViaR-based Forecast of Oil Price Risk, Energy Economics 31(4), 511–518
  D. Huang, B. Yu, F. J. Fabozzi and M. Fukushima
  
• Exercise Strategies for American Options under Ambiguity, IMW-Working Paper 421 (2009)
  T. Chudjakow and J. Vorbrink
  
• Fine Properties of Stochastic Evolution Equations and Their Applications, PhD thesis (2009)
  W. Liu
  
• Harnack inequalities and applications for stochastic equations, PhD thesis (2009)
  S.-X. Ouyang
  
• Harnack inequality and applications for stochastic evolution equations with monotone drifts, J. Evol. Equ. 9 (2009), 747–770
  W. Liu
  
• Individual based model with competition in spatial ecology, SIAM J. Math. Anal. 41(1) (2009), 297–317
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy
  
• Markov evolutions and hierarchical equations in the continuum. I. One-component systems, J. Evol. Equ. 9(2) (2009), 197–233
  D. Finkelshtein, Y. Kondratiev, M. J. Oliveira
  
• Measures on two-component configuration spaces, Condensed Matter Physics 12(1) (2009), 5–18
  D. Finkelshtein
  
• Noise induced temporal patterns in populations of globally coupled oscillators, Proceedings of INDS’09 - Second International Workshop on Nonlinear Dynamics and Synchronization (2009), 194–197, art. no. 5227997
  M.-O. Hongler, R. Filliger, P. Blanchard, J. Rodriguez
  
• On the probabilistic longest common subsequence problem for sequences of independent blocks, PhD thesis (2009)
  F. Torres
  
• On the stochastic p-Laplace equation, J. Math. Anal. Appl. 360 (2009), 737–751
  W. Liu
  
• Pricing Corporate Bonds in Structural Models under CEV Process, Acta Math. Applicatae Sinica, English Series (2009)
  C. Qu
  
• Ranking Measures and Loss Functions in Learning to Rank, Advances in Neural Information Processing Systems 22 (NIPS) (2009), 315–323
  W. Chen, T.-Y. Liu, Y. Lan, Z.-M. Ma, and H. Li
  
• Regulation mechanisms in spatial stochastic development models, J. Stat. Phys. 136(1) (2009), 103–115
  D. Finkelshtein, Y. Kondratiev
  
• Relation between “no broadcasting” for noncommuting states and “no local broadcasting” for quantum correlations, Phys. Rev. A 79 (2009), 054305
  S. Luo, N. Li and X. Cao
  
• Relative entropy between quantum ensembles, Periodica Math. Hungarica 59 (2009), 223–237
  S. Luo, N. Li and X. Cao
  
• Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders, Insurance: Mathematics and Economics 45(3) (2009), 459–465
  Yo. Song, J.-A. Yan
  
• Scenery reconstruction, PhD thesis (2009)
  A. Pachon Pinzon
  
• Soliton-like waves of nuclear burning in the neutron multiplicating media: (theory and computational approach), PhD thesis (2009)
  O. A. Byegunova
  
• Stochastic Comparison and Preservation of Positive Correlations for Lévy-type Processes, Acta Math. Sinica 25 (2009), 741–758
  J. Wang
  
• Stochastic dynamics with singular lower order terms in finite and infinite dimensions, PhD thesis (2009)
  P. Jin
  
• Stochastic monotonicity and positive correlations of a type of particle systems on Polish spaces, Acta Mathematica Sinica, Chinese Series, 52(2) (2009), 309–314
  G.-Q. Lan
  
• Symmetric Lévy type operators, Acta Math. Sinica 25 (2009), 39–46
  J. Wang
  
• “Quantum” chaos and stability condition of soliton-like waves of nuclear burning in neutronmultiplicating media (2009)
  V. D. Rusov, E. P. Linnik, V. A. Tarasov, T. N. Zelentsova, I. V. Sharf, S. A. Chernezhenko, O. A. Byegunova
  
• A Note on Fundamental Limit of Quantum Dynamics Rate, Commun. Theor. Phys. 54 (2010), 661–662
  S. Fu, N. Li and S. Luo
  
• A Note on Fundamental Limit of Quantum Dynamics Rate, Commun. Theor. Phys. 54 (2010), 661–662
  S. Fu, N. Li and S. Luo
  
• BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space, Comptes Rendus Mathematique 348(21–22) (2010), 1175–1178
  M. Röckner, R. Zhu, X. Zhu
  
• BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space, Comptes Rendus Mathematique 348(21–22) (2010), 1175–1178
  M. Röckner, R. Zhu, X. Zhu
  
• Decorrelating capabilities of operations with application to decoherence, Phys. Rev. A 82 (2010), 052122
  S. Luo, S. Fu and N. Li
  
• Decorrelating capabilities of operations with application to decoherence, Phys. Rev. A 82 (2010), 052122
  S. Luo, S. Fu and N. Li
  
• Entire solutions of hydrodynamical equations with exponential dissipation, Comm. Pure Appl. Math. 293 (2010), 519–543
  C. Bardos, U. Frisch, W. Pauls, S. S. Ray, E. Titi
  
• Fluctuation of the longest common subsequence for sequences of independent blocks (2010)
  H. Matzinger, F. Torres
  
• Geometric measure of quantum discord, Phys. Rev. A. 82 (2010), 034302
  S. Luo and S. Fu
  
• Global effect of quantum states induced by locally invariant measurements, Europhys. Lett. 92(2) (2010)
  S. Luo and S. Fu
  
• Gluing and coupling, Statistics & Probability Letters 80(15–16) (2010), 1196–1199
  S.-X. Ouyang
  
• Harnack inequalities for some Lévy processes, Potential Anal. 32 (2010), 275–303
  A. Mimica
  
• Interacting particle systems on graphs, PhD thesis (2010)
  N. Tekmen
  
• Invariance of subspaces under the solution flow of SPDE, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 13(1) (2010), 87–98
  W. Liu
  
• Large deviations for stochastic evolution equations with small multiplicative noise, Appl. Math. Optim. 61(1) (2010), 27–56
  W. Liu
  
• On complex singularities of the 2D Euler equation at short times, Physica D 239 (2010), 1159–1169
  W. Pauls
  
• On notions of harmonicity for non-symmetric Dirichlet form, Science China Mathematics 53(6) (2010), 1407–1420
  Z.-M. Ma, R. Zhu, X. Zhu
  
• On notions of harmonicity for non-symmetric Dirichlet form, Science China Mathematics 53(6) (2010), 1407–1420
  Z.-M. Ma, R. Zhu, X. Zhu
  
• Perturbation of generalized Dirichlet forms by signed smooth measures and the associated Markov processes, Acta Math. Sci. Ser. A Chin. Ed. 30 (2010)
  X. Han, L. Ma and X. Yang
  
• Two-layer Generalization Analysis for Ranking Using Rademacher Average, Advances in Neural Information Processing Systems 23 (NIPS) (2010), 370–378
  W. Chen, T.-Y. Liu, and Z.-M. Ma
  
• Variational convergence of nonlinear partial differential operators on varying Banach spaces, PhD thesis (2010)
  J. Tölle
  
• Vlasov scaling for stochastic dynamics of continuous systems, J. Stat. Phys. 141(1) (2010), 158–178
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy
  
• American options with multiple priors in continuous time, IMW-Working Paper 448 (2011)
  J. Vorbrink
  
• An elementary proof of the L1 log-Sobolev inequality for Poisson point processes, Statist. Probab. Lett. 81 (2011), 16–19
  C.-S. Deng and Y. Song
  
• Binary jumps in continuum. I. Equilibrium processes and their scaling limits, J. Math. Phys. 52 (2011), 063304, 1–25
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy, E. Lytvynov
  
• Binary jumps in continuum. II. Non-equilibrium process and a Vlasov-type scaling limit, J. Math. Phys. 52 (2011), 113301, 1–27
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy, E. Lytvynov
  
• Classical and quantum correlative capacities of quantum systems, Phys. Rev. A 84 (2011), 042124
  N. Li and S. Luo
  
• Complex manifolds for the Euler equations: a hierarchy of ODEs and the case of vanishing angle in two dimensions, Fluid Dyn. Research 43 (2011), 025505
  A. Gilbert, W. Pauls
  
• Conservative stochastic dynamics of continuous interacting particle systems, PhD thesis, Bielefeld University (2011), 102 pages
  C. Berns
  
• Decoherence and measurement-induced correlations, Phys. Rev. A 84 (2011), 052309
  S. Luo and N. Li
  
• Evaluation of a Bayesian coalescent method of species delimitation, Systematic Biology 29 (2011), 325–335
  C. Zhang, D.-X. Zhang, T. Zhu, Z. Yang
  
• Efficient simulation under a population genetics model of carcinogenesis, Bioinformatics 27 (2011), 837–843
  T. Zhu, Y. Hu, Z.-M. Ma, D.-X. Zhang, T. Li, Z. Yang
  
• Functional evolutions for homogeneous stationary death-immigration spatial dynamics, Methods Funct. Anal. Topology 17(4) (2011), 300–318
  D. Finkelshtein
  
• Harnack inequalities and applications for multivalued stochastic evolution equations, Infin. Dimens. Anal. Quantum Probab. Relat. Top 14(2) (2011), 261–278
  S.-X. Ouyang
  
• Local universality of repulsive particle systems and random matrices, PhD thesis, Bielefeld University (2011), 77 pages
  M. Venker
  
• Martingale solutions and Markov selection of stochastic 3D Navier-Stokes equations with jump, J. Differential Equations 250 (2011) 2737–2778
  Z. Dong, J. Zhai
  
• Maximum Nonlocal Effects of Quantum States, Int. J. Quantum Inf. 9(7) (2011), 1–12
  S. Fu and S. Luo
  
• Measurement-Induced Nonlocality, Phys. Rev. Lett. 106 (2011), 120401
  S. Luo and S. Fu
  
• On Some Classes of Birth and Death Processes in Continuum, PhD thesis (2011)
  L. Derdziuk
  
• On stochastic processes driven by ballistic noise sources, Proceedings of MSAST 2011 - Mathematical Sciences for Advancement of Science and Technology (2011)
  M.-O. Hongler, R. Filliger, P. Blanchard, J. Rodriguez
  
• Ornstein–Uhlenbeck equations with time-dependent coefficients and Levy noise in finite and infinite dimensions, Journal of Evolution Equations 11(4) (2011), 959–993
  F. Knäble
  
• Overconfidence on Public Information, Economics Letters (SSCI) 112 (2011), 239–242
  D. Zhou
  
• Properties of hitting times for G-martingales and their applications, Stochastic Process. Appl. 121(8) (2011), 1770–1784
  Yo. Song
  
• Random attractors for a class of stochastic partial differential equations driven by general additive noise, J. Differential Equations 251(4–5) (2011), 1225–1253
  B. Gess, W. Liu, M. Röckner
  
• Remarks on non-symmetric perturbed Dirichlet forms and switching identities, Chinese J. Appl. Probab. Statist. 27(3) (2011), 305–311
  X. Han, L. Ma and X. Yang
  
• Saddlepoint approximation for moments of random variables, Frontiers of Mathematics in China 6(6) (2011), 1265–1284
  K. Zhao, X. Cheng, J. Yang
  
• Some properties on G-evaluation and its applications to G-martingale decomposition, Sci. China Math. 54(2) (2011), 287–300
  Yo. Song
  
• Some remarks on Li-Sinai type solutions of the Burgers equation, Journal of Physics A: Mathematical and Theoretical 44 (2011), 285209
  W. Pauls
  
• Stochastic Analysis related to Gamma measures - Gibbs perturbations and associated diffusions, PhD thesis (2011)
  D. Hagedorn
  
• Stochastic flows induced by stochastic partial differential equations, PhD thesis, Bielefeld University (2011), 183 pages
  B. Gess
  
• The global random attractor for a class of stochastic porous media equations, Comm. Partial Differential Equations 36(3) (2011), 446–469
  W.-J. Beyn, B. Gess, P. Lescot, M. Röckner
  
• The Quantumness of Quantum Ensembles, Theor. Math. Phys. 169(3) (2011), 1723–1738
  S. Luo, N. Li and S. Fu
  
• Valuation of Cross-Currency Bermudan Swaption, Chinese Journal of Applied Probability and Statistics 27(4) (2011), 425–434
  Z. Du, D. Zhang
  
• Valuation of financial contingent claims in the presence of model uncertainty, PhD thesis (2011)
  J. Vorbrink
  
• Vlasov scaling for the Glauber dynamics in continuum, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14(4) (2011), 537–569
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy
  
• Web Markov Skeleton Processes and Their Applications, Tohoku Math. J(2) 63(4) (2011), 665–695
  Y. Liu, Z.-M. Ma and C. Zhou
  
• A new look at the Lagrange method for continuous-time stochastic optimization, Science China Mathematics 55(11) (2012), 2247–2258
  X. Cheng, J.-A. Yan
  
• An approximative approach for construction of the Glauber dynamics in continuum, Math. Nachr. 285(2–3) (2012), 223–235
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy, E. Zhizhina
  
• Analysis of nonautonomous Ornstein–Uhlenbeck processes with cadlag paths, PhD thesis (2012)
  F. Knäble
  
• BSDE associated with generalized Dirichlet forms: finite dimensional case, IDAQP 15(4) (2012), 40 pages
  R. Zhu
  
• Coherent Price Systems and Uncertainty-Neutral Valuation, IMW Working Paper 464 (2012)
  P. Beißner
  
• Convergence Analysis for Weighted Joint Strategy Fictitious Play in Generalized Second Price Auction, Proceedings of the 10th Conference on Web and Internet Economics (WINE) (2012), 489– 495
  L. Yao, W. Chen, and T.-Y. Liu
  
• Correlation functions evolution for the Glauber dynamics in continuum, Semigroup Forum 85 (2012), 289–306
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy
  
• Coverage of Random Discs Driven by Poisson Processes, Probability Approximations and Beyond. Lecture Notes in Statistics 205 (2012), 43–59
  G.-L. Lan, Z.-M. Ma, S.-Y. Sun
  
• Elliptic law for real random matrices (2012)
  A. Naumov
  
• Evaluating a Geometric Measure of Quantum Discord, Theor. Math. Phys. 171(3) (2012), 870–878
  S. Luo and S. Fu
  
• Further Study on Web Markov Skeleton Processes, Stochastic Analysis and Applications to Finance, Essays in Honour of Jia-An Yan (2012), 313–339
  Y. Liu, Z.-M. Ma and C. Zhou
  
• General approach to the fluctuations problem in random sequence comparison (2012)
  J. Lember, H. Matzinger, F. Torres
  
• Glauber dynamics in the continuum via generating functionals evolution, Complex Analysis and Operator Theory 6(4) (2012), 923–945
  D. Finkelshtein, Y. Kondratiev, M. J. Oliveira
  
• Harnack inequalities and applications for Ornstein-Uhlenbeck semigroups with jumps, Potential Analysis 36(2) (2012), 301–315
  S.-X. Ouyang, M. Röckner, F.-Y. Wang
  
• Harnack inequalities for subordinate Brownian motions, Electron. J. Probab. 17(37) (2012), 1–23
  P. Kim, A. Mimica
  
• Heat kernel estimates for jump processes with small jumps of high intensity, Potential Anal. 36 (2012), 203–222
  A. Mimica
  
• Integrated Sequence-Structure Motifs Suffice to Identify microRNA Precursors, PLOS ONE 7(3), (2012)
  X. Liu, S. He, G. Skogerbo, F. Gong, R. Chen
  
• Kawasaki dynamics in the continuum via generating functionals evolution, Methods Funct. Anal. Topology 18(1) (2012), 55–67
  D. Finkelshtein, Y. Kondratiev, M. J. Oliveira
  
• Markov Jump Dynamics with Additive Intensities in Continuum: State Evolution and Vlasov Scaling, SFB 701 Preprint 12042 (2012)
  C. Berns, Y. Kondratiev, O. Kutoviy
  
• Nelkin scaling for the Burgers equation and the role of high-precision calculations, Phys. Rev. E 85 (2012), 015391
  S. Chakraborty, U. Frisch, W. Pauls, S. S. Ray
  
• Overconfidence, Public Disclosure and Long-lived Information, Economics Letters (SSCI) 116 (2012), 626–630
  D. Zhou
  
• Quantifying correlations via the Wigner-Yanase skew information, Phys. Rev. A 85 (2012), 032117
  S. Luo, S. Fu and C. H. Oh
  
• Quantifying non-Markovianity via correlations, Phys. Rev. A 86 (2012), 044101
  S. Luo, S. Fu and S. Hong
  
• Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise (Concise announcement of the results), Comptes Rendus Mathematique 350(5–6) (2012), 299–302
  B. Gess
  
• SDE and BSDE on Hilbert spaces: applications to quasi-linear evolution equations and the asymptotic properties of the stochastic quasi-geostrophic equation, PhD thesis (2012)
  R. Zhu
  
• SDE in infinite dimensions: the reflection problem and the stochastic quasi-geostrophic equation, PhD thesis (2012)
  X. Zhu
  
• Semigroup approach to birth-and-death stochastic dynamics in continuum, J. of Funct. Anal. 262(3) (2012), 1274–1308
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy
  
• Stochastic analysis with the Gamma measure - moving a dense set, Theor. Probability and Math. Statist. 85 (2012), 149–158
  D. Hagedorn
  
• Strong solutions for stochastic partial differential equations of gradient type, Journal of Functional Analysis 263(8) (2012), 2355–2383
  B. Gess
  
• Subgraph with orthogonal (0, f )-factorization in (0, mf − k + 1-graph, Operations Research Transactions 16(3) (2012), 132–138
  L. Xiao, Y. Liu
  
• The rate of the convergence of the mean score in random sequence comparison, Ann. Appl. Probab. 22(3) (2012), 1046–1058
  H. Matzinger, J. Lember, F. Torres
  
• The Size Distribution of Peninsula in a Random Graph Process, Recent Advances in Computer Science and Information Engineering. Lecture Notes in Electrical Engineering 127 (2012), 47–54
  L. Xiao, W. Ren, G. Yan
  
• The stochastic quasi-geostrophic equation (Announcement), IDAQP 15(1) (2012), 6 pages
  M. Röckner, R. Zhu, X. Zhu
  
• The stochastic quasi-geostrophic equation (Announcement), IDAQP 15(1) (2012), 6 pages
  M. Röckner, R. Zhu, X. Zhu
  
• The stochastic reflection problem on a convex set of a Hilbert space and BV functions in a Gelfand triple, The Annals of Probability 40(4) (2012), 1759–1794
  M. Röckner, R. Zhu, X. Zhu
  
• The stochastic reflection problem on a convex set of a Hilbert space and BV functions in a Gelfand triple, The Annals of Probability 40(4) (2012), 1759–1794
  M. Röckner, R. Zhu, X. Zhu
  
• Uniqueness of the representation for G-martingales with finite variation, Electron. J. Probab. 17(24) (2012)
  Yo. Song
  
• Uniqueness of weighted Sobolev spaces with weakly differentiable weights, J. Funct. Anal. 263(10) (2012), 3195–3223
  J. Tölle
  
• Universality of some models of random matrices and random processes, PhD thesis (2012)
  A. Naumov
  
• Weak log-Sobolev and Lp weak Poincaré inequalities for general symmetric forms, Front. Math. China. 7 (2012), 1059–1071
  C.-S. Deng and Y. Song
  
• A Game-theoretic Machine Learning Approach for Revenue Maximization in Sponsored Search, Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI) (2013), 206–212
  D. He, W. Chen, L. Wang, and T.-Y. Liu
  
• A perturbative probabilistic approach to quantum many-body systems, J. Stat. Mech. (2013), P04002
  A. Di Stefano, M. Ostilli, C. Presilla
  
• A Theoretical Analysis of NDCG Type Ranking Measures, Proceedings of the 26th Annual Conference on Learning Theory (COLT) (2013), 25–54
  Y. Wang, L. Wang, Y. Li, D. He, W. Chen, and T.-Y. Liu
  
• An operator approach to Vlasov scaling for some models of spatial ecology, Methods Funct. Anal. Topology 19(2) (2013), 108–126
  D. Finkelshtein, Y. Kondratiev, O. Kutoviy
  
• Analysis of jump processes with nondegenerate jumping kernels, Stoch. Process. Appl. 123 (2013), 629–650
  M. Kassmann, A. Mimica
  
• Channel-state duality, Phys. Rev. A 87, 022310 (2013)
  M. Jiang, S. Luo and S. Fu
  
• Comparing quantum cloning: A Fisher-information perspective, Phys. Rev. A 88 (2013), 042121
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• Construction of a State Evolution for Kawasaki Dynamics in Continuum, Analysis and Mathematical Physics 3(2) (2013), 97–117
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• Detect taxonomy-specific pathway associations with environmental factors using metagenomic data, Proceedings of the 7th International Conference on Systems Biology 2013 (ISB), 139–144
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• Dynamical behavior of endomorphisms on certain invariant sets, Mathematica Slovaca 63(1) (2013), 135–142
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• Elliptic law for random matrices, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (1) (2013), 31–38, 48
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• Entanglement detection via quantum Fisher information, Phys. Rev. A 88 (2013), 014301
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• Entrance laws of generalized Ornstein-Uhlenbeck processes and asymptotic strong Feller property for non-autonomous semigroups, PhD thesis (2013)
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• Establishment and fecundity in spatial ecological models: statistical approach and kinetic equations, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 16(2) (2013), 1350014, 24 pages
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• Exponential Convergence for Semilinear SDEs Driven by Lévy Processes on Hilbert Spaces
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• Finite speed of propagation for stochastic porous media equation, SIAM J. Math. Anal. 45(5) (2013), 2734–2766
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• Gibbs states over the cone of discrete measures, Journal of Functional Analysis 264(11) (2013), 2550–2583
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• Glauber dynamics in continuum: a constructive approach to evolution of states, Discrete and Cont. Dynam. Syst. - Ser A. 33(4) (2013), 1431–1450
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• Harnack inequality and Hölder regularity estimates for a Lévy process with small jumps of high intensity, J. Theor. Probab. 26 (2013), 329–348
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• Hierarchy of Correlations via Lüders Measurements, Int. J. Mod. Phys. B 27 (2013), 1345026
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• Integrability of zero-dimensional replica field theories at β = 1, Phys. Rev. E 88 (2013), 030101(R)
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• Introduction to quantum correlations, Physics 42(08) (2013)
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• Irrational Confidence, Imperfect and Long-lived Information, International Review of Economics and Finance (SSCI) 27 (2013), 383–405
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• Item-based Top-K Influential Users Discovering in Social Networks, Proceedings of the 13th IEEE International Conference on Data Mining Workshops (ICDMW) (2013), 780–787
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• Kawasaki dynamics in continuum: micro- and mesoscopic descriptions, Journal of Dynamics and Differential Equations 25(4) (2013), 1027–1056
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• Large deviation principles for the stochastic quasi-geostrophic equation, Stoch. Proc. Appl. 123(8) (2013), 3299–3327
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• Large deviations principle of the random field Curie-Weiss models, J. Phys. A: Math. Theor. 46(12) (2013), 125004
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• Markov evolutions and hierarchical equations in the continuum. II: Multicomponent systems, Reports Math. Phys. 71(1) (2013), 123–148
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• Microeconomic Theory of Financial Markets under Volatility Uncertainty, PhD thesis (2013)
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• Noise and Delays in Adaptive Interacting Oscillatory Systems, PhD thesis (2013)
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• On convolutions on configuration spaces. I. Spaces of finite configurations. II. Spaces of locally finite configurations, Ukrainian Math. J. 64(11) (2013), 1752–1775, 64(12) (2013), 1919–1944
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• On generalized infinite Bernoulli convolutions with overlaps and their fractal properties, Theor. Probability and Math. Statistics 87 (2013), 99–115
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• On Stochastic Processes Driven By Ballistic Noise Sources, Contemporary Topics in Mathematics and Statistics with Applications (Editors: A. Adhikari, M. R. Adhikari, Y. P. Chaubey), Asian Books Private, New Delhi (2013), 1–29
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• On the Hausdorff dimension faithfulness and the Cantor series expansion (2013)
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• Online Learning for Auction Mechanism in Bandit Setting, Decision Support Systems 56 (2013), 379–386
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• Optimal stopping under ambiguity in continuous time, Mathematics and Financial Economics 7(1) (2013), 29–68
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• Particle Systems with Repulsion Exponent β and Random Matrices, Electron. Commun. Probab. 18(83) (2013), 1–12
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• Personalized Influence Maximization on Social Networks, Proceedings of the 22nd International Conference on Information and Knowledge Management (CIKM) (2013), 199–208
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• Products of Independent Quaternion Ginibre Matrices and their Correlation Functions, J. Phys. A 46 (2013), 265201
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• Products of Rectangular Random Matices: Singular values and Progressive Scattering, Phys. Rev. E 88 (2013), 052118
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• Proportion of gaps and fluctuations of the optimal score in random sequense comparison, Limit Theorems in Probability, Statistics and Number Theory, Springer Proceedings in Mathematics Statistics 42 (2013), 207–233
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• Radner Equilibria under Ambiguous Volatility, IMW Working Paper 493 (2013)
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• Random Attractors for Degenerate Stochastic Partial Differential Equations, J. Dynam. Differential Equations 25(1) (2013), 121–157
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• Random attractors for singular stochastic partial evolution equations, J. Differential Equations 255(3) (2013), 524–559
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• Self-Shaping Attractors for Coupled Limit Cycle Oscillators, Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering 483 (Editors: K. Kyamakya, W. A. Halang, W. Mathis, J. C. Chedjou, Z. Li), Springer, Berlin (2013), 97–115
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• Stochastic evolution of a continuum particle system with dispersal and competition: Microand mesoscopic description, The European Physical Journal Special Topics 216(1) (2013), 107–116
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• The estimates of heat kernels with Neumann boundary conditions, Potential Analysis 38(2) (2013), 549–572
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• Time-Delayed Interactions in Networks of Self-Adapting Hopf Oscillators, ISRN Mathematical Analysis (2013), ID 816353, 9 pages
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• UBLF: An Upper Bound Based Approaches to Discover Influential Nodes in Social Networks, Proceedings of the 13th IEEE International Conference on Data Mining (ICDM) (2013), 907–916
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• Uniqueness results for non-negative solutions of quasi-linear inequalities on Riemannian manifolds, SFB 701 Preprint 13068 (2013)
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• (Non-)Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty (2014)
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• A mathematical framework for the analysis of spatial-temporal point processes, Theoretical Ecology 7(1) (2014), 101–113
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• A new method for modeling coalescent processed with recombination, BMC Bioinformatics 15:273 (2014)
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• A new method for modeling coalescent processes with recombination, BMC Bioinformatics 15:273 (2014)
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• A note on Monge-Kantorovich Problem, Statistics and Probability Letters 84 (2014), 204–211
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• A note on stochastic semilinear equations and their associated Fokker-Planck equations, J. Math. Anal. Appl. 415(1) (2014), 83–109
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• A note on stochastic semilinear equations and their associated Fokker-Planck equations, J. Math. Anal. Appl. 415(1) (2014), 83–109
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• A probabilistic approach to Neumann problems of semilinear elliptic PDEs with singular coefficients, Stochastic Processes and their Applications 124(7) (2014), 2442–2478
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• A Research on the Hedging Strategy of CSI 300 Index Futures Based on Mean-Fractal Dimension, J. Futures and Financial Derivatives 70 (2014), 36–48
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• A survey on bogoliubov generating functionals for interacting particle systems in the continuum, In From Particle Systems to Partial Differential Equations, volume 75 of Springer Proceedings in Mathematics & Statistics, pp. 161–177. Springer-Verlag Berlin Heidelberg, 2014
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• A transformation of Markov jump processes and applications in genetic study, Discrete Contin. Dyn. Syst. 34(12) (2014), 5061–5084
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• Adaptation of Oscillatory Systems in Networks - A Learning Signal Approach, System Research and Information Technologies 2014(2) (2014), 53–67
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• Agent Behavior Prediction and Its Generalization Analysis, Proceedings of the 28th International Association for the Advancement of Artificial Intelligence Conference (AAAI) (2014), 1300–1306
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• Agent Behavior Prediction and Its Generalization Analysis, Proceedings of the 28th International Association for the Advancement of Artificial Intelligence Conference (AAAI) (2014), 1300–1306
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• Asymptotic Expansions in Classical and Free Probability, PhD thesis (2014)
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• Asymptotic Expansions in Free Limit Theorems (2014)
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• Cell Growth and Size Homeostasis in Silico, Biophysical Journal 106 (2014), 991–997
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• Density behavior of spatial birth-and-death stochastic evolution of mutating genotypes under selection rates, Russ. J. Math. Phys. 21(4) (2014), 450–459
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• Derivative formula and exponential convergence for semilinear SPDEs driven by Lévy processes, Statist. Probab. Lett. 89 (2014), 99–109
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• Exponential convergence rates of second quantization semigroups and applications, Q. J. Math. 65 (2014), 349–364
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• Financial markets with volatility uncertainty, Journal of Mathematical Economics 53 (2014), 64–78
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• Generalized Second Price Auction with Probabilistic Broad Match, Proceedings of the 15th ACM Conference on Economics and Computation (EC) (2014), 39–56
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• Green function estimates for subordinate Brownian motions: stable and beyond, Trans. Amer. Math. Soc. 366 (2014), 4383–4422
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• Harnack inequalities for SDEs driven by subordinate Brownian motions, J. Math. Anal. Appl. 417 (2014), 970–978
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• Harnack inequality on configuration spaces: the coupling approach and a unified treatment, Stochastic Process. Appl. 124 (2014), 220–234
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• Intrinsic scaling properties for nonlocal operators II. 2015
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• Limit Theorems for Multivariate Lacunary Systems (2014)
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• Limit theorems for two classes of random matrices with dependent entries, Probability Theory and its Applications, 59(1) (2014), 61–80
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• Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise, Stochastic Processes and their Applications 124(5) (2014), 1974–2002
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• Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise, Stochastic Processes and their Applications 124(5) (2014), 1974–2002
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• Local Universality of Repulsive Particle Systems and Random Matrices, The Annals of Probability 42(6) (2014), 2207–2242
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• Malliavin matrix of degenerate SDE and gradient estimate, Electrical Journal of Probability 19 (2014), Article 73
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• Markov jump processes in modeling coalescent with recombination, Ann. Statist. 42(4) (2014), 129–161
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• Markov jump processes in modeling coalescent with recombination, Ann. Statist. 42(4) (2014), 129–161
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• Maximum likelihood implementation of an isolation-with-migration model with three species for testing speciation with gene flow, Molecular Biology and Evolution 29 (2014), 3131–3142
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• Microeconomic foundations of representative agent models by means of ultraproducts, IMW Working Paper 514 (2014)
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• Multi-valued, singular stochastic evolution inclusions, J. Math. Pures Appl. 101(6) (2014), 789–827
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• On a Cameron-Martin type quasi-invariance theorem and applications to subordinate Brownian motions (2014)
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• On an aggregation in birth-and-death stochastic dynamics, Nonlinearity 27 (2014), 1105–1133
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• On harmonic functions of symmetric Lévy processes, Ann. Inst. H. Poincaré Probab. Statist. 50(1) (2014), 214–235
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• On non-negative solutions of the inequality ∆u + uσ ≤ 0 on Riemannian manifolds, Comm. Pure Appl. Math. 67(8) (2014), 1336–1352
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• On shift Harnack inequalities for subordinate semigroups and moment estimates for Lévy processes (2014)
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• On the Law of Large Numbers for the empirical measure process of Generalized Dyson Brownian motion
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• On the Probabilistic Behaviour of Multivariate Lacunary Systems, PhD thesis (2014)
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• On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds, SFB 701 Preprint 14036 (2014)
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• Optimal extraction of information from two spins, Phys. Rev. A 89 (2014), 042110
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• Permanental processes from products of complex and quaternionic induced Ginibre ensembles, Random Matrices 3 (2014), 1450014
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• piRNA Identification Based on Motif Discovery, Mollar Boym 10(12) (2014), 3075–3080
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• Poincaré and weak Poincaré inequalities for the mixed Poisson measures, Acta Math. Sin. (Engl. Ser.) 30 (2014), 1719–1728
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• Probabilistic Star Discrepancy Bounds for Lacunary Point Sets (2014)
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• Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise, The Annals of Probability 42(2) (2014), 818–864
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• Random matrix theory of quantum transport in chaotic cavities with non ideal leads (2014)
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• Random Parametric Resonance in Time-Dependent Networks of Adaptive Frequency Oscillators, Discontinuity, Nonlinearity, and Complexity, special issue on Mathematics of Multi-level Anticipatory Complex Systems 3(3) (2014), 347–365
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• Regularity of density for SDEs driven by degenerate Lévy noises (2014)
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• Refining a randomized post-optimization method on covering arrays, 2014 IEEE International Conference on Software Testing, Verification, and Validation Workshops (ICSTW 2014)
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• Sampling Dilemma: Towards Effective Data Sampling for Click Prediction in Sponsored Search, Proceedings of 7th ACM Conference on Web Search and Data Mining (WSDM) (2014), 103–112
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• Spectral Distribution of Non-independent Random Matrix Ensembles induced by Lacunary Systems (2014)
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• Sponsored Search Auctions: Recent Advances and Future Directions, ACM Transactions on Intelligent Systems and Technology 5(4) (2014)
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• Star Discrepancy Bounds of Double Infinite Matrices induced by Lacunary Systems (2014)
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• Statistical dynamics of continuous systems: perturbative and approximative approaches, Arab. J. Math. (2014), online first
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• Stochastic calculus of fractional Lévy processes, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 17(1) (2014), 1450006
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• Stochastic nonlinear Schrdinger equation, PhD thesis (2014)
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• Stochastic nonlinear Schr¨dinger equations (2014)
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• Stochastic Nonlinear Schr¨dinger Equations with Linear Multiplicative Noise: Rescaling Approach, J. Nonlinear Sci. 24(3) (2014), 383–409
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• Stochastic nonlinear Schrödinger equations: no blow-up in the non-conservative case (2014)
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• Tail Paradox, Partial identifiability and influential priors in Bayesian branch length inference, Molecular Biology and Evolution 60 (2014), 747–761
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• The impact of the Rate Prior on Bayesian Estimation of Divergence Times with Multiple Loci, Systematic Biology 63 (2014), 555–565
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• Thermal transport through non ideal Andreev chaotic cavities (2014)
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• Uniqueness of equilibrium states in some models of interacting particle systems, PhD thesis (2014)
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• Uniqueness result for non-negative solutions of semi-linear inequalities on Riemannian manifolds, J. Math. Anal. Appl. 419(1) (2014), 643–661
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• Uniqueness result for nonnegative solutions of a large class of inequalities on Riemannian manifolds, SFB 701 Preprint 14037 (2014)
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• Universality for products of random matrices I: Ginibre and truncated unitary cases
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• Volume Growth and Uniqueness of Nonnegative Solutions of Differential Inequalities on Manifolds, PhD thesis (2014)
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• Weak Approximation of G-expectation, IMW Working Paper 503 (2014)
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• Weak Commutation Relations and Eigenvalue Statistics for Products of Rectangular Random Matrices, Phys. Rev. E 89 (2014), 032106
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• Brownian Equilibrium under Knightian Uncertainty, Mathematics and Financial Economics 9(1) (2015), 39–56
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• BSDE associated with generalized Dirichlet forms: finite dimensional case, Forum Mathematicum 27(1) (2015), 201–253
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• Characterization of the uncertainty of divergence time estimation under the relaxed molecular clock with multiple loci, Systematic Biology 64(2) (2015), 267–280
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• Dynamic Consistent α–Maxmin Expected Utility, IMW Working Paper 535 (2015)
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• Dynamical Widom–Rowlinson model and its mesoscopic limit, J. Stat. Phys. 158(1) (2015), 57–86
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• E-Tree: an efficient indexing structure for ensemble models on data streams, IEEE Transactions on Knowledge and Data Engineering (TKDE) 27(2) (2015), 461–474
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• Equilibrium diffusion on the cone of discrete Radon measures (2015)
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• Generalization Analysis for Game-Theoretic Machine Learning, Proceedings of the 29th International Association for the Advancement of Artificial Intelligence Conference (AAAI) (2015), 2089–2095
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• Generalization Analysis for Game-Theoretic Machine Learning, Proceedings of the 29th International Association for the Advancement of Artificial Intelligence Conference (AAAI) (2015), 2089–2095
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• Gibbs Fields: Uniqueness and Decay of Correlations. Revisiting Dobrushin and Pechersky (2015)
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• Gibbs Measures on Marked Configuration Spaces: Existence and Uniqueness (2015)
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• Gradient estimates and coupling property for semilinear SDEs driven by jump processes, Sci. China Math. 58 (2) (2015), 447–458
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• Influence Maximization in Big Network: An Incremental Algorithm for Streaming Subgraph Influence Spread Estimation. IJCAI Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, July 2015. S. 2076-2082
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• Large Deviations for SPDEs of jump type, Stochastics and Dynamics 15(4) (2015)
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• Limit theorems for two classes of random matrices with Gaussian elements, Journal of Mathematical Sciences 204(1) (2015), 140–147
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• Lyapunov exponents for products of rectangular real, complex and quaternionic Ginibre matrices, J. Phys. A 48 (2015), 155204
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• Markov birth-and-death dynamics of populations (2015)
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• Mechanism Learning Based on Mechanism Induced Data, Proceedings of the 29th International Association for the Advancement of Artificial Intelligence Conference (AAAI) (2015), 4037–4041
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• On minimal singular values of random matrices with correlated entries. Random Matrices: Theory and Applications, Vol. 04, No. 02, 1550006 (2015)
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• Quasi-regular semi-Dirichlet forms and beyond, Festschrift Masatoshi Fukushima, In honor of Masatoshi Fukushima’s Sanju (2015), 421–452
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• Recent exact and asymptotic results for products of independent random matrices (2015)
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• Stochastic Partial Differential Equations: An Introduction. (Universitext) Springer, Heidelberg (2015), 266 pages. 978-3319223537
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• Sub- and supercritical stochastic quasi-geostrophic equation, The Annals of Probability 43(3) (2015), 1202–1273
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• Sub- and supercritical stochastic quasi-geostrophic equation, The Annals of Probability 43(3) (2015), 1202–1273
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• The Dirichlet problem for nonlocal operators, Mathematische Zeitschrift 279(3–4) (2015), 779–809
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• The statistical dynamics of a spatial logistic model and the related kinetic equation, Math. Models Methods Appl. Sci. 25(2) (2015), 343–370
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• Fukushima type decomposition for semi-Dirichlet forms. Tohoku Math. Journal, (2) Volume 68, Number 1 (2016), 1-27
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• Strong Feller properties for degenerate SDEs with jumps. Ann. Inst. Henri Poincar Prob. Stat., Volume 52, Number 2 (2016), 888-897
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• Strong Feller properties for degenerate SDEs with jumps. Annales de l’Institut Henri Poincaré (B) Probabilités et Statistiques, Volume 52, Number 2 (2016), 888-897
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• Time inhomogeneous generalized Mehler semigroups and skew convolution equations. Forum Mathematicum, Band 28, Heft 2, S. 339–376, 2016
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