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The asymptotic behavior of a divergent linear birth and death process

Published online by Cambridge University Press:  01 July 2016

Martha J. Siegel
Martha J. Siegel*
Affiliation:
Towson State College, Baltimore, Maryland
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Abstract

We consider a birth and death process with Q-matrix of rates qm,m + 1 = mβ, qm,m − 1 = mδ, qm,m = – m(β + δ) and qm,n = 0 otherwise. We assume that 0 < δ < β and β – δ = 1. The asymptotic behavior of first-arrival time at state n given that the process is at state m at time zero is expressed in terms of polynomials and it is shown that if m < n and m is large that the first-arrival time is close to log n/m with high probability.

Keywords

BIRTH AND DEATH PROCESSESASYMPTOTIC GROWTHFIRST-ENTRY TIMES
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 2 , June 1976 , pp. 315 - 338
Copyright
Copyright © Applied Probability Trust 1976 

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