一般状态空间连续时间Markov过程的常返性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 860-873.

一般状态空间连续时间Markov过程的常返性

朱志锋(),黄弘*

^{湖北工程学院数学与统计学院湖北孝感 432000}

收稿日期:2019-09-11 出版日期:2021-06-26 发布日期:2021-06-09
通讯作者: 黄弘 E-mail:376574200@qq.com
作者简介:朱志锋, E-mail: 376574200@qq.com
基金资助:
湖北省教育厅项目(B2019150);孝感市自然科学计划项目(XGKJ2020010046);湖北工程学院教研项目(2018C19)

Recurrence of Continuous Time Markov Process in General State Space

Zhifeng Zhu(),Hong Huang*

^{School of Mathematics and Statistics, Hubei Engineering University, Hubei Xiaogan 432000}

Received:2019-09-11 Online:2021-06-26 Published:2021-06-09
Contact: Hong Huang E-mail:376574200@qq.com
Supported by:
the Hubei Education Department Foundation(B2019150);the NSF of Xiaogan(XGKJ2020010046);the Teaching Research Project of Hubei Engineering University(2018C19)

摘要/Abstract

摘要：

该文定义了连续时间Markov过程的一致非常返集，并讨论了连续时间Markov过程一致非常返集的判定方法.得到了Ψ不可约条件下连续时间Markov过程的常返性一些结论，也得到了一些与细集相关的常返性结果.

关键词: Markov过程, Ψ不可约, 常返性

Abstract:

In this paper, the uniform extraordinary recurrent set of continuous time Markov processes is defined, and the determination method of uniform extraordinary recurrent set of continuous time Markov processes is discussed. Some conclusions on the recurrence of continuous time Markov processes with Ψ irreducibility are obtained, and some recurrence results related to petite sets are also obtained.

Key words: Markov process, Ψ Irreducible, Recurrence

中图分类号:

O211.4

朱志锋,黄弘. 一般状态空间连续时间Markov过程的常返性[J]. 数学物理学报, 2021, 41(3): 860-873.

Zhifeng Zhu,Hong Huang. Recurrence of Continuous Time Markov Process in General State Space[J]. Acta mathematica scientia,Series A, 2021, 41(3): 860-873.

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