用耦合方法研究Markov过程的f-遍历

朱志锋, 张绍义

数学学报 ›› 2022, Vol. 65 ›› Issue (6) : 1137-1142.

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PDF(379 KB)
数学学报 ›› 2022, Vol. 65 ›› Issue (6) : 1137-1142. DOI: 10.12386/A20190048
论文

用耦合方法研究Markov过程的f-遍历

    朱志锋1, 张绍义2
作者信息 +

f-ergodicity of Markov Process by Coupling Method

    Zhi Feng ZHU1, Shao Yi ZHANG2
Author information +
文章历史 +

摘要

该文先研究基本耦合,得到全变差范数与基本耦合的一个等式.然后利用此等式研究一般状态空间下连续时间Markov过程的遍历性.对遍历的连续时间Markov过程,增加条件πf)<,利用耦合方法证明了存在满的吸收集,使得连续时间Markov过程在其上是f-遍历的.

Abstract

We first study the basic coupling and obtain an equation between total variation norm and the basic coupling. Then by use this equation we investigate the ergodicity property of continuous time Markov processes in general state space. For an ergodic continuous-time Markov processes, adding condition π(f)<, by using the coupling method, there exists the full absorption set, such that the continuous time Markov processes are f-ergodic on it.

关键词

Markov过程 / 基本耦合 / 全变差范数 / f-遍历

Key words

Markov processes / the basic coupling / total variation norm / f-ergodic

引用本文

导出引用
朱志锋, 张绍义. 用耦合方法研究Markov过程的f-遍历. 数学学报, 2022, 65(6): 1137-1142 https://doi.org/10.12386/A20190048
Zhi Feng ZHU, Shao Yi ZHANG. f-ergodicity of Markov Process by Coupling Method. Acta Mathematica Sinica, Chinese Series, 2022, 65(6): 1137-1142 https://doi.org/10.12386/A20190048

参考文献

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[11] Zhang S. L., Stochastic Stability of General State Space Jump Processes, Doctoral Dissertation of Hubei University, Wuhan, 2014.

基金

湖北省自然科学基金青年项目(2021CFB275);应用数学湖北省重点实验室(湖北大学)开放基金(HBAM202104)
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