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Taboo extinction, sojourn times, and asymptotic growth for the Markovian birth and death process

Published online by Cambridge University Press:  20 February 2017

W. A. O'n. Waugh
W. A. O'n. Waugh*
Affiliation:
University of Toronto
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Abstract

A well-known result in the theory of branching processes provides an asymptotic expression for the population size (valid for large times) in terms of a single random variable, multiplied by a deterministic exponential growth factor. In the present paper this is generalized to a class of size-dependent population models. The work is based on the series of sojourn times. An essential tool is the use of probabilities conditional upon non-extinction (taboo probabilities).

Keywords

MARKOV BIRTH AND DEATH PROCESSTABOO STATESSOJOURN TIMESBRANCHING PROCESSESASYMPTOTIC POPULATION GROWTHEXTINCTION OF POPULATIONSTOCHASTIC LAGEXPLOSIVE MARKOV PROCESSES

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972 , pp. 486 - 506
Copyright
Copyright © Applied Probability Trust 1972 

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