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Symmetric jump processes and their heat kernel estimates

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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 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Zhen-Qing Chen

  2. Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, China

    Zhen-Qing Chen

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  1. Zhen-Qing Chen
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Correspondence to Zhen-Qing Chen.

Additional information

This work was supported by National Science Foundation of USA (Grant No. DMS-0600206)

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Chen, ZQ. Symmetric jump processes and their heat kernel estimates. Sci. China Ser. A-Math. 52, 1423–1445 (2009). https://doi.org/10.1007/s11425-009-0100-0

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  • DOI: https://doi.org/10.1007/s11425-009-0100-0

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