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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-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 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
Externally published	Yes
Event	International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 - Osaka, Japan Duration: 22 Aug 2022 → 26 Aug 2022

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	22/08/22 → 26/08/22

Keywords

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

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

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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title = "Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results",

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{\textquoteright} method developed in [10].",

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

author = "Chen, {Zhen Qing} and Panki Kim and Takashi Kumagai and Jian Wang",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.; International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 ; Conference date: 22-08-2022 Through 26-08-2022",

year = "2022",

doi = "10.1007/978-981-19-4672-1_5",

language = "English",

isbn = "9789811946714",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "63--83",

editor = "Zhen-Qing Chen and Masayoshi Takeda and Toshihiro Uemura",

booktitle = "Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima{\textquoteright}s Beiju, IWDFRT 2022",

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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, 22/08/22. 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 › peer-review

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AU - Chen, Zhen Qing

AU - Kim, Panki

AU - Kumagai, Takashi

AU - Wang, Jian

PY - 2022

Y1 - 2022

N2 - 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].

AB - 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].

KW - Diffusion process with jumps

KW - Heat kernel estimate

KW - Inner uniform domain

KW - Parabolic Harnack inequality

KW - Symmetric Dirichlet form

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BT - Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022

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Chen ZQ, Kim P, Kumagai T, Wang J. Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results. In Chen ZQ, 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

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

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