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连续时间马氏链中拟平稳分布和不变分布之间的关系 被引量：1

On the Relationship between μ-Invariant Distribution and Quasi-stationary Distributions for Continuous-time Markov Chains
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摘要 Van Doorn (1991)说明在一个有吸收态的生灭过程中 ,如何用过程的转移概率来确定拟平稳分布 .Nair和 Pollett (1933)把它推广到由一个不可约类 C和一个吸收态 0 ,并且 0从可到不可约类 C的连续时间马氏链。 Van Doorn (1991) explained how quasi stationary distributions for an absorbing birth death process could be determined from the transition rates of the process. Nair and Pollett (1993) extended it to deal with an arbitrary continuous time Markov chain over a countable state space, consisting of an irreducible class, C , and an absorbing state, 0, which is accessible from C . In this paper, we discuss the relationship between μ invariant distributions and quasi stationary distributions for continuous time Markov chains.
作者 梅其祥 林祥
机构地区 中南大学铁道校区现代教育技术中心 中南大学铁道校区科研所
出处 《数学理论与应用》 2001年第2期26-29,共4页 Mathematical Theory and Applications
关键词 Q-函数 拟平稳分布 μ-不变分布 连续时间马氏链 转移概率 Q function Quasi stationary distribution μ invariant distribution
分类号 O211.62 [理学—概率论与数理统计]
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参考文献1

  • 1P. K.Pollett (1986) On the Equivalence of -invariant Measures for the Minimal Process and its q-matrix[].Stochastic Processes and Their Applications.

同被引文献8

  • 1E. A. Van Doom. Quasi - Stationary Distributions and Conver- gence to Quasi - Stationarity of Birth - Death Processes [ J ]. Adv. Appl. Probab. 1991(23) : 683 -700.
  • 2E. A. Van Doom. On Associated Polynomials and Decay Rates of Birth- Death Processes [ J]. J. Math. Anal. Appl. 2003 (278) : 500 -511.
  • 3E. A. Van Doom, and Zeifman, A.I. Birth - death Proeasses with Killing[J]. Statist. Probab. Lett. 2005(72):33-42.
  • 4E. A. Van Doom, and Zeifman, A.I. (2005). Extinction Prob- ability in a Birth -Death Process with Killing[ J]. Appl. Prob- ab. 2005(42) : 185 -198.
  • 5P. C. Sehrijner and E. A. van Doom. Quasi-Stationary Distri- butions For Birth- Death Processes with Killing[ J]. Journal of Applied Mathematics and Stochastic Analysis. 2006( 1 ) : 1 - 18.
  • 6Li, Q. L. Stochastic Integral Funetionals and Quasi - stationary Distributions in Stochastic Models [ D ]. Institute of Applied Mathematics. Chinese Academy of Seienees,Beijing,1997.
  • 7李泉林.博士后出站报告[R].中国科学院自动化研究所,1999.
  • 8J.N. Darroeh and E. Seneta . On Quasi -stationary Distribu- tions in Absorbing Discrete - time Finite Markov Chains [ J ]. Appl. Probab. 1965 (2):88 - I00.

引证文献1

数学理论与应用
2001年 第2期

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