Science in China Series A: Mathematics

, Volume 52, Issue 7, pp 1423–1445

Symmetric jump processes and their heat kernel estimates

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 processdiffusion with jumpspseudo-differential operatorDirichlet forma prior Hölder estimatesparabolic Harnack inequalityglobal and Dirichlet heat kernel estimatesLévy system

MSC(2000)

60J3547G3060J4531C0531C2560J75

Copyright information

© Science in China Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.Department of MathematicsBeijing Institute of TechnologyBeijingChina