Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results

Zhen Qing Chen, Panki Kim, Takashi Kumagai*, Jian Wang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

This article gives an overview of some recent progress in the study of sharp two-sided estimates for the transition density of a large class of Markov processes having both diffusive and jumping components in metric measure spaces. We summarize some of the main results obtained recently in [11, 18] and provide several examples. We also discuss new ideas of the proof for the off-diagonal upper bounds of transition densities which are based on a generalized Davies’ method developed in [10].

Original languageEnglish
Title of host publicationDirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022
EditorsZhen-Qing Chen, Masayoshi Takeda, Toshihiro Uemura
PublisherSpringer
Pages63-83
Number of pages21
ISBN (Print)9789811946714
DOIs
Publication statusPublished - 2022
Externally publishedYes
EventInternational Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 - Osaka, Japan
Duration: 22 Aug 202226 Aug 2022

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume394
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Dirichlet Forms and Related Topics, IWDFRT 2022
Country/TerritoryJapan
CityOsaka
Period22/08/2226/08/22

Keywords

  • Diffusion process with jumps
  • Heat kernel estimate
  • Inner uniform domain
  • Parabolic Harnack inequality
  • Symmetric Dirichlet form

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Chen, Z. Q., Kim, P., Kumagai, T., & Wang, J. (2022). Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results. In Z.-Q. Chen, M. Takeda, & T. Uemura (Eds.), Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022 (pp. 63-83). (Springer Proceedings in Mathematics and Statistics; Vol. 394). Springer. https://doi.org/10.1007/978-981-19-4672-1_5