论费勒马尔可夫链的不变分布及其在随机切换动力系统中的应用

IF 1.5 1区数学 Q2 STATISTICS & PROBABILITY

Probability Theory and Related Fields Pub Date : 2024-08-12 DOI:10.1007/s00440-024-01307-y

Michel Benaïm, Oliver Tough

{"title":"论费勒马尔可夫链的不变分布及其在随机切换动力系统中的应用","authors":"Michel Benaïm, Oliver Tough","doi":"10.1007/s00440-024-01307-y","DOIUrl":null,"url":null,"abstract":"<p>We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows.</p>","PeriodicalId":20527,"journal":{"name":"Probability Theory and Related Fields","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching\",\"authors\":\"Michel Benaïm, Oliver Tough\",\"doi\":\"10.1007/s00440-024-01307-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows.</p>\",\"PeriodicalId\":20527,\"journal\":{\"name\":\"Probability Theory and Related Fields\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Theory and Related Fields\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00440-024-01307-y\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Theory and Related Fields","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00440-024-01307-y","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

我们引入了一些简单的条件，以确保紧凑黎曼流形上的费勒马尔可夫链的不变分布是绝对连续的，且相对于黎曼度量具有下半连续、连续或光滑密度。这适用于通过随机组合映射得到的马尔可夫链，以及通过随机切换流得到的片断确定性马尔可夫过程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On invariant distributions of Feller Markov chains with applications to dynamical systems with random switching

We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the Riemannian measure. This is applied to Markov chains obtained by random composition of maps and to piecewise deterministic Markov processes obtained by random switching between flows.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Probability Theory and Related Fields 数学-统计学与概率论

CiteScore

3.70

自引率

5.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Probability Theory and Related Fields publishes research papers in modern probability theory and its various fields of application. Thus, subjects of interest include: mathematical statistical physics, mathematical statistics, mathematical biology, theoretical computer science, and applications of probability theory to other areas of mathematics such as combinatorics, analysis, ergodic theory and geometry. Survey papers on emerging areas of importance may be considered for publication. The main languages of publication are English, French and German.