吸收的随机单调马氏链的拟平稳分布

朱依霞

doi:2016.03.006

吸收的随机单调马氏链的拟平稳分布

doi: 2016.03.006

朱依霞^,

1.
湘潭大学数学与计算科学学院, 湖南湘潭 411105

基金项目:

国家自然科学基金(11371301); 湖南省研究生科研创新项目(CX2013B251)

详细信息

作者简介:
作者简介: 朱依霞, 女, 博士研究生,研究方向为概率论与数理统计.

通讯作者:
朱依霞, 女, 博士研究生,研究方向为概率论与数理统计.

中图分类号: O211.6
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- 被引次数: 0
出版历程
- 收稿日期: 2015-05-12
- 刊出日期: 2016-05-25

Quasi-stationary distributions for absorbing stochastically monotone Markov chains

ZHU Yi-Xia^,

摘要

摘要: 本文考虑吸收的随机单调马氏链在生存时间内的某些极限定理.主要考虑三种类型的拟平稳分布:平稳条件的拟平稳分布、双重极限条件的拟平稳分布和极限条件平均比值的拟平稳分布.研究了随机单调马氏链的三类拟平稳分布的唯一性和吸引域问题.在某种条件下，这三类拟平稳分布都是唯一的,并且所有的初始分布都在这个唯一的拟平稳分布的吸引域里面. 最后,将主要结论应用到生灭过程.
- 吸引域 /
- 拟平稳分布 /
- 马氏链 /
- 生灭过程
Abstract: In this paper, we prove some limit theorems for absorbing stochastically monotone Markov chain during its lifetime. The emphases are on the stationary conditional, doubly limiting conditional and limiting conditional mean ratio quasi-stationary distributions. We study the uniqueness and domain of attraction of three types of quasi-stationary distributions for stochastically monotone Markov chains. A sufficient condition for the uniqueness of the three types of quasi-stationary distributions is given in our main results and under this condition, the unique quasi-stationary distribution attracts all initial distributions. We apply the main results to birth and death processes.
- domain of attraction quasi-stationary distributionMarkov chainbirth anddeath process /

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参考文献(1)

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