吸收的随机单调马氏链的拟平稳分布

doi:2016.03.006

华东师范大学学报(自然科学版) ›› 2016, Vol. 2016 ›› Issue (3): 48-59.doi: 2016.03.006

吸收的随机单调马氏链的拟平稳分布

朱依霞

湘潭大学数学与计算科学学院, 湖南湘潭 411105

收稿日期:2015-05-12 出版日期:2016-05-25 发布日期:2016-09-22
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. E-mail:yxz@xtu.edu.cn
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.
基金资助:
国家自然科学基金(11371301);
湖南省研究生科研创新项目(CX2013B251)

Quasi-stationary distributions for absorbing stochastically monotone Markov chains

ZHU Yi-Xia

Received:2015-05-12 Online:2016-05-25 Published:2016-09-22

摘要/Abstract

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.

关键词: 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.

Key words: domain of attraction, quasi-stationary distribution;Markov chain;birth anddeath process

中图分类号:

O211.6

朱依霞. 吸收的随机单调马氏链的拟平稳分布[J]. 华东师范大学学报(自然科学版), 2016, 2016(3): 48-59.

ZHU Yi-Xia. Quasi-stationary distributions for absorbing stochastically monotone Markov chains[J]. Journal of East China Normal University(Natural Sc, 2016, 2016(3): 48-59.

参考文献

[1]POLLETT P K. Quasi stationary distributions: A bibliography R/OL].(2015-03-13)2015-03-30].http://www.maths.uq.edu.au/\simpkp/papers/qsds/qsds.pdf.
[2]DARROCH J N, SEBETA E. On quasi-stationary distributions in absorbing discrete-time finite Markov chains J]. Journal of Applied Probability, 1965(2): 88-100.
[3]DARROCH J N, SEBETA E. On quasi-stationary distributions in absorbing continuous-time finite Markov chains J]. Journal of Applied Probability, 1967(4): 192-196.
[4]SENETA E, VERE-JONES D. On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states[J]. Journal of Applied Probability, 1966(3): 403-434.
[5]FLASPOHLER D C. Quasi-stationary distributions for absorbing continuous-time denumerable Markov chains J]. Annals of the Institute of Statistical Mathematics, 1974, 26(1): 351-356.
[6]PAKES A G. Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state J]. Advances in Applied Probability, 1995, 27: 120-145.
[7]KINGMAN J F C. The exponential deacy of Markov transition probabilities J]. Proceedings of the London Mathematical Society,1963, 13: 337-358.
[8]ANDERSON W J. Continuous-Time Markov Chains: An Applications-Oriented Approach M]. New York: Springer, 1991.
[9]VAN DOORN E A. Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes J]. Advances in Applied Probability, 1991, 23: 683--700.
[10]ZHANG H J, ZHU Y X. Domain of attraction of the quasistationary distribution for birth and death processes J]. Journal of Applied Probability, 2013, 50: 114-126.
[11]CHEN A Y, ZHANG H J. Existence, uniqueness, and constructions for stochastically monotone Q-processes J]. Southeast Asian Bulletin of Mathematics, 1999, 23: 559-583.
[12]JACKA S D, ROBERS G O. Weak convergrnce of conditioned processes on a countable state space J]. Journal of Applied Probability, 1995,32: 902-916.
[13]VERE-JONES D. Ergodic Properties of non-negative matrices I J].Pacific Journal of Mathematics, 1967, 22(2): 361-385.
[14]KARLIN S, MCGREGOR J L. The classification of birth and death processes J]. Transactions of the American Mathematical Society,1957, 86: 366-400.
[15]KARLIN S, TAYLOR H M. A First Course in Stochastic Processes M].2nd ed. New York: Academic press, 1975.

吸收的随机单调马氏链的拟平稳分布

Quasi-stationary distributions for absorbing stochastically monotone Markov chains

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