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Birth and death processes in random environments with feedback

Published online by Cambridge University Press:  14 July 2016

Richard Cornez
Richard Cornez*
Affiliation:
University of Colorado at Colorado Springs
*
∗Postal address: Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, CO 80933–7150, USA.
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Abstract

A generalization of a birth and death chain in a random environment (Yn, Zn) is developed allowing for feedback to the environmental process (Yn). The resulting process is then known as a birth and death chain in a random environment with feedback. Sufficient conditions are found under which the (Zn) process goes extinct almost surely or has strictly positive probability of non-extinction.

Keywords

MARKOV CHAINUNIFORMLY φ-RECURRENTBIRTH AND DEATH CHAIN

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987, pp. 25 - 34
Copyright
Copyright © Applied Probability Trust 1987 

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References

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