Growth rates for pure birth Markov chains

Athreya, K. B. (2008) Growth rates for pure birth Markov chains Statistics & Probability Letters, 78 (12). pp. 1534-1540. ISSN 0167-7152

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A pure birth Markov chain is a continuous time Markov chain {Z(t):t≥0} with state space S≡{0,1,2,...} such that for each i≥0 the chain stays in state i for a random length of time that is exponentially distributed with mean λ-1i and then jumps to (i+1). Suppose b(.) is a function from (0,∞)→(0,∞) that is nondecreasing and ↑∞. This paper addresses the two questions: (1) Given {λi}i≥0 what is the growth rate of Z(t)? (2) Given b(.) does there exist {λi}} such that Z(t) grows at rate b(t)?

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
ID Code:1124
Deposited On:05 Oct 2010 12:53
Last Modified:12 May 2011 09:39

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