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

^*此作品的通讯作者

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

摘要

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].

源语言	英语
主期刊名	Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022
编辑	Zhen-Qing Chen, Masayoshi Takeda, Toshihiro Uemura
出版商	Springer
页	63-83
页数	21
ISBN（印刷版）	9789811946714
DOI	https://doi.org/10.1007/978-981-19-4672-1_5
出版状态	已出版 - 2022
已对外发布	是
活动	International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022 - Osaka, 日本期限: 22 8月 2022 → 26 8月 2022

出版系列

姓名	Springer Proceedings in Mathematics and Statistics
卷	394
ISSN（印刷版）	2194-1009
ISSN（电子版）	2194-1017

会议

会议	International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022
国家/地区	日本
市	Osaka
时期	22/08/22 → 26/08/22

访问文件

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

其它文件与链接

链接到 Scopus 的出版物

引用此

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

Chen, Zhen Qing ; Kim, Panki ; Kumagai, Takashi 等. / 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. 编辑 / Zhen-Qing Chen ; Masayoshi Takeda ; Toshihiro Uemura. Springer, 2022. 页码 63-83 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{0a2ac87b4a8e44c5896342cd0d167e4e,

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",

address = "Germany",

}

Chen, ZQ, Kim, P, Kumagai, T & Wang, J 2022, Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results. 在 Z-Q Chen, M Takeda & T Uemura (编辑), Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022. Springer Proceedings in Mathematics and Statistics, 卷 394, Springer, 页码 63-83, International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022, Osaka, 日本, 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 等.
Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022. 编辑 / Zhen-Qing Chen; Masayoshi Takeda; Toshihiro Uemura. Springer, 2022. 页码 63-83 (Springer Proceedings in Mathematics and Statistics; 卷 394).

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

TY - GEN

T1 - Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps

T2 - International Conference on Dirichlet Forms and Related Topics, IWDFRT 2022

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

UR - http://www.scopus.com/inward/record.url?scp=85137985775&partnerID=8YFLogxK

U2 - 10.1007/978-981-19-4672-1_5

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

M3 - Conference contribution

AN - SCOPUS:85137985775

SN - 9789811946714

T3 - Springer Proceedings in Mathematics and Statistics

SP - 63

EP - 83

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

A2 - Chen, Zhen-Qing

A2 - Takeda, Masayoshi

A2 - Uemura, Toshihiro

PB - Springer

Y2 - 22 August 2022 through 26 August 2022

ER -

Chen ZQ, Kim P, Kumagai T, Wang J. Two-Sided Heat Kernel Estimates for Symmetric Diffusion Processes with Jumps: Recent Results. 在 Chen ZQ, Takeda M, Uemura T, 编辑, Dirichlet Forms and Related Topics - In Honor of Masatoshi Fukushima’s Beiju, IWDFRT 2022. Springer. 2022. 页码 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

摘要

出版系列

会议

访问文件

其它文件与链接

指纹

引用此