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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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S01677...

Related URL: http://dx.doi.org/10.1016/j.spl.2008.01.016

## Abstract

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^{-1}_{i} 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 {λ_{i}}_{i≥0} what is the growth rate of Z(t)? (2) Given b(.) does there exist {λ_{i}}} such that Z(t) grows at rate b(t)?

Item Type: | Article |
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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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