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 | |
【 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.
【 授权许可】
Free
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
10_1016_j_jmaa_2011_06_085.pdf | 129KB | download |