期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:385
Domain of attraction of the quasi-stationary distribution for the linear birth and death process
Article
Zhang, Hanjun1  Liu, Wenbo1 
[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China
关键词: Linear birth and death process;    Domain of attraction;    Quasi-stationary distribution;    Probability generating function;   
DOI  :  10.1016/j.jmaa.2011.06.085
来源: Elsevier
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【 摘 要 】

We obtain a sufficient condition for an initial distribution to be in the domain of attraction of the quasi-stationary distribution for a linear birth and death process by two methods. that is. let M = < m(i), i = 1,2, ...> be a probability distribution with Sigma(i) im(i) < infinity, then lim(t ->infinity) P(M)(X(t) = j vertical bar T > t) = v(j), where v(j) is a geometric distribution with parameter lambda/mu. The first method acquires the results by computing directly while the second method bases on the theory of probability generating function. (C) 2011 Elsevier Inc. All rights reserved.

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