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

Zhen Qing Chen; Panki Kim; Takashi Kumagai; Jian Wang

doi:10.1007/978-981-19-4672-1_5

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

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022
Editors	Zhen-Qing Chen, Masayoshi Takeda, Toshihiro Uemura
Publisher	Springer
Pages	63-83
Number of pages	21
ISBN (Print)	9789811946714
DOIs	https://doi.org/10.1007/978-981-19-4672-1_5
Publication status	Published - 2022
Event	International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 - Osaka, Japan Duration: 2022 Aug 22 → 2022 Aug 26

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	394
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022
Country/Territory	Japan
City	Osaka
Period	22/8/22 → 22/8/26

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/978-981-19-4672-1_5

Cite this

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

Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps : Recent Results. / Chen, Zhen Qing; Kim, Panki; Kumagai, Takashi et al.

Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022. ed. / Zhen-Qing Chen; Masayoshi Takeda; Toshihiro Uemura. Springer, 2022. p. 63-83 (Springer Proceedings in Mathematics and Statistics; Vol. 394).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Chen, ZQ, 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. Springer Proceedings in Mathematics and Statistics, vol. 394, Springer, pp. 63-83, International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022, Osaka, Japan, 22/8/22. https://doi.org/10.1007/978-981-19-4672-1_5

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

Chen, Zhen Qing ; Kim, Panki ; Kumagai, Takashi et al. / Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps : Recent Results. Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022. editor / Zhen-Qing Chen ; Masayoshi Takeda ; Toshihiro Uemura. Springer, 2022. pp. 63-83 (Springer Proceedings in Mathematics and Statistics).

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

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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