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Birth and death processes with random environments in continuous time

Published online by Cambridge University Press:  14 July 2016

Robert Cogburn and
William C. Torrez
Robert Cogburn*
Affiliation:
University of New Mexico
William C. Torrez*
Affiliation:
University of California, Riverside
*
∗ Postal address: Department of Mathematics and Statistics, The University of New Mexico, Albuquerque, NM 87131, U.S.A.
∗∗ Postal address: Department of Statistics, University of California, Riverside, CA 92521, U.S.A.
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Abstract

A generalization to continuous time is given for a discrete-time model of a birth and death process in a random environment. Some important properties of this process in the continuous-time setting are stated and proved including instability and extinction conditions, and when suitable absorbing barriers have been defined, methods are given for the calculation of extinction probabilities and the expected duration of the process.

Keywords

BIRTH AND DEATH PROCESSINSTABILITYEXTINCTIONMARKOV CHAINS IN RANDOM ENVIRONMENTSBIVARIATE DIFFERENCE EQUATION

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981, pp. 19 - 30
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Partially supported by a Ford Foundation post-doctoral fellowship.

References

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