AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home AIMS Mathematics Article
PDF (242.4 KB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline
Research Article | Open Access

Exponentially quasi-mixing ergodicity for symmetric Markov processes

Saixia Liao1( ), Hanjun Zhang2, Huasheng Li3
School of Mathematical Sciences, Changsha Normal University, Changsha, Hunan 410100, China
School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
School of Mathematics and Statistics, Hainan University, Haikou, Hainan 570000, China
Show Author Information

Abstract

In this paper, we focused on the quasi-mixing limits of symmetric Markov processes. Under mild assumptions, we proved that (intrinsic) ultracontractivity of the transition semigroup implied (uniformly) exponentially quasi-mixing ergodicity of its associated process. As a by-product, we demonstrated that the underlying process exhibited (uniformly) exponentially quasi-ergodicity, (uniformly) exponentially fractional quasi-ergodicity, and (uniformly) mean-ratio quasi-ergodicity being proportional to time.

Keywords

symmetric Markov processintrinsic ultracontractivityquasi-mixing limitquasi-ergodicityfractional quasi-ergodicitymean-ratio quasi-ergodicity
CLC number: 37A30, 47D07, 60J25, 60J35

References

【1】
【1】
 
 
Crossref Google Scholar
AIMS Mathematics
Volume 11 Issue 6,
June 2026
Pages 17009-17021
DOI: 10.3934/math.2026696

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
Liao S, Zhang H, Li H. Exponentially quasi-mixing ergodicity for symmetric Markov processes. AIMS Mathematics, 2026, 11(6): 17009-17021. https://doi.org/10.3934/math.2026696

3

Views

0

Downloads

0

Crossref

0

Web of Science

0

Scopus
Received: 17 March 2026
Revised: 01 June 2026
Accepted: 08 June 2026
Published: 15 June 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)