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 contribution

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
EventInternational Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 - Osaka, Japan
Duration: 2022 Aug 222022 Aug 26

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
Period22/8/2222/8/26

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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