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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
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

Chung, K. L. (1964) The general theory of Markov processes according to Doeblin. Z. Wahrscheinlichkeitsth. 2, 230–254.Google Scholar
Neveu, J. (1970) Chaînes de Markov. Textos de Matematica 19, Instituto de Matematica, Univ. Federal de Pernambuco.Google Scholar
Orey, S. (1971) Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities, Van Nostrand Mathematical Studies 34, Van Nostrand, Princeton, NJ.Google Scholar
Torrez, W. (1978) The birth and death chain in a random environment. Ann. Prob. 6, 1026–1043.Google Scholar