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arXiv · 0904.2796

Symmetric Jump Processes and their Heat Kernel Estimates

Zhen-Qing Chen
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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 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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Zhen-Qing Chen. 2009-04-17. Symmetric Jump Processes and their Heat Kernel Estimates. https://doi.org/10.1007/s11425-009-0100-0

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