Science in China Series A: Mathematics

, Volume 52, Issue 7, pp 1423–1445

Symmetric jump processes and their heat kernel estimates

Authors

    • Department of MathematicsUniversity of Washington
    • Department of MathematicsBeijing Institute of Technology
Article

DOI: 10.1007/s11425-009-0100-0

Cite this article as:
Chen, Z. Sci. China Ser. A-Math. (2009) 52: 1423. doi:10.1007/s11425-009-0100-0

Abstract

We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes (or equivalently, a class of symmetric integro-differential operators). We focus on the sharp two-sided estimates for the transition density functions (or heat kernels) of the processes, a priori Hölder estimate and parabolic Harnack inequalities for their parabolic functions. In contrast to the second order elliptic differential operator case, the methods to establish these properties for symmetric integro-differential operators are mainly probabilistic.

Keywords

symmetric jump process diffusion with jumps pseudo-differential operator Dirichlet form a prior Hölder estimates parabolic Harnack inequality global and Dirichlet heat kernel estimates Lévy system

MSC(2000)

60J35 47G30 60J45 31C05 31C25 60J75

Copyright information

© Science in China Press and Springer-Verlag GmbH 2009