Singular integral operators and stochastic processes (A02)

• Subject Area: Mathematics
• Term: from 2017 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 317210226

We develop a mathematical theory for nonlocal and discrete differential operators, which are related to Markov processes on subsets of the Euclidean space or graphs. We focus on results which are crucial for an understanding of the underlying dynamics independent of regularity assumptions on the state space or inhomogeneities of the medium. In this project, we study the following two interrelated parts, which go beyond current research and provide several new mathematical challenges: (I) Nonlocal operators with logarithmic order of differentiability and (II) Nonlocal operators and Markov processes on graphs.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1283: Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications
• Applicant Institution: Universität Bielefeld
• Project Head: Professor Dr. Rolf Moritz Kaßmann