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Recurrence criteria for multi-dimensional Markov chains and multi-dimensional linear birth and death processes

Published online by Cambridge University Press:  01 July 2016

Harry Kesten
Harry Kesten*
Affiliation:
Cornell University
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Abstract

Criteria are established for a discrete-time Markov process {Xn}n≧0 in Rd to have strictly positive, respectively zero, probability of escaping to infinity. These criteria are mainly in terms of the mean displacement vectors μ(y) = E{Xn+1|Xn = y} – y, and are essentially such that they force a deterministic process w.p.1 to move off to infinity, respectively to return to a compact set infinitely often. As an application we determine of most two-dimensional birth and death processes with rates linearly dependent on the population, whether they can escape to infinity or not.

Keywords

MULTI-DIMENSIONAL MARKOV PROCESSMULTI-DIMENSIONAL BIRTH AND DEATH PROCESSTRANSIENTRECURRENTESCAPE TO INFINITY
Type
Research Article
Information
Advances in Applied Probability , Volume 8 , Issue 1 , March 1976 , pp. 58 - 87
Copyright
Copyright © Applied Probability Trust 1976 

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