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Projekt Druckansicht

GRK 1132:  Stochastik und Modellierung realer Systeme

Fachliche Zuordnung Mathematik
Förderung Förderung von 2006 bis 2014
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 772176
 
Erstellungsjahr 2015

Zusammenfassung der Projektergebnisse

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.

Projektbezogene Publikationen (Auswahl)

 
 

Zusatzinformationen

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