Symmetric jump processes and their heat kernel estimates
By Zhen-Qing Chen. 2009
51 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Finance
View Paper: https://www.semanticscholar.org/paper/c5db3b933be04971b31ef4935ece7e2fb5d35d67
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In Applied Mathematics
- Longjie Xie
- Xicheng Zhang
- Eryan Hu
- Zhen-Qing Chen
- T. Grzywny
- Michael Röckner
- Panki Kim
- Takashi Kumagai
In Computational Theory and Mathematics
- Longjie Xie
- Xicheng Zhang
- Eryan Hu
- Zhen-Qing Chen
- Panki Kim
- Takashi Kumagai
- Renming Song
- M. Kassmann
In Finance
- Longjie Xie
- Xicheng Zhang
- Zhen-Qing Chen
- Eryan Hu
- Renming Song
- Feng-Yu Wang
- Michael Röckner
- Panki Kim
Citations in the corpus
- Heat kernels for non-symmetric diffusion operators with jumps (2016, background): “We refer the reader to the survey articles [5, 19] and the references therein on the study of heat kernels for symmetric non-local operators.”
- Regularity theory for parabolic nonlinear integral operators (2011, unknown): “For the time-dependent case, a version of the result was proved by Komatsu [17], using the corresponding Nash scheme (see also Chen [10]).”