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On calculating extinction probabilities for branching processes in random environments

Published online by Cambridge University Press:  14 July 2016

William E. Wilkinson
William E. Wilkinson*
Affiliation:
Duke University, Durham, North Carolina
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Extract

Consider a discrete time Markov chain {Zn} whose state space is the non-negative integers and whose transition probability matrix ║Pij║ possesses the representation where {Pr}, r = 1,2,…, is a finite or denumerably infinite sequence of non-negative real numbers satisfying , and , is a corresponding sequence of probability generating functions. It is assumed that Z0 = k, a finite positive integer.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 3 , December 1969 , pp. 478 - 492
Copyright
Copyright © Applied Probability Trust 

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References

Gantmacher, F. R. (1959) Applications of the Theory of Matrices. Interscience Publishers, New York.Google Scholar
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Smith, W. L. (1968) Necessary conditions for almost sure extinction of a branching process with random environment. Ann. Math. Statist. 39, 2136–2140.CrossRefGoogle Scholar
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