Project A8: Fine properties of long-range operators and processes

Summary:

In this project, we study fine properties of nonlocal operators and their corresponding stochastic processes. The operators under consideration may be regarded as generalizations of powers of the Laplace operator (with exponent less than one) and alpha-stable jump processes to a natural class of integro-differential operators and jump processes. To some extent, one can consider these objects as nonlocal analogs to diffusion operators and diffusions. There has recently been an increasing interest in such non-local operators and corresponding jump processes from various different viewpoints. The project concentrates on fine properties such as pointwise estimates. Both, techniques and problems, are related to analysis, partial differential equations and stochastic processes at the same time.

Recent Preprints: