Symmetric Jump Processes and their Heat Kernel Estimates

Details Symmetric Jump Processes and their Heat Kernel Estimates Symmetric Jump Processes and their Heat Kernel Estimates

2009-04-17

arxiv.org/abs/0904.2796v1

Mathematics

Probability

To appear in Science in China Series A: Mathematics

Scientific paper

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 Holder 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.

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