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A continuous time Markov branching model with random environments

Published online by Cambridge University Press:  01 July 2016

Norman Kaplan
Norman Kaplan*
Affiliation:
University of California, Berkeley
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Abstract

A population model is constructed which combines the ideas of a discrete time branching process with random environments and a continuous time non-homogeneous Markov branching process. The extinction problem is considered and necessary and sufficient conditions for extinction are determined. Also discussed are limit theorems for what corresponds to the supercritical case.

Keywords

BRANCHING PROCESSBRANCHING PROCESS WITH RANDOM ENVIRONMENTRANDOM ENVIRONMENTSTATIONARY ERGODIC PROCESSCONTINUOUS TIME NON-HOMOGENEOUS MARKOV BRANCHING PROCESS

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 1 , April 1973 , pp. 37 - 54
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Athreya, K. B. and Karlin, S. (1971) Branching processes with random environments, I: Extinction probability. Ann. Math. Statist. 42, 1499–1521.Google Scholar
[2] Athreya, K. B. and Karlin, S. (1971) Branching processes with random environments II: Limit theorems. Ann. Math. Statist. 42, 1843–1858.Google Scholar
[3] Cramér, H. and Leadbetter, M. R. (1966) Stationary and Related Stochastic Processes. John Wiley and Sons, Inc., New York.Google Scholar
[4] Halmos, P. R. (1956) Lectures in Ergodic Theory. Chelsea Publishing Co., New York.Google Scholar
[5] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin.Google Scholar
[6] Ito, K. (1963–4) Stationary Processes Seminar Notes. Stanford University.Google Scholar
[7] Kaplan, N. (1971) Some results about multidimensional branching processes with random environments. Submitted to Ann. Math. Statist. Google Scholar
[8] Savits, T. H. (1971) Branching Markov processes in a random environment. To appear.Google Scholar
[9] Smith, W. L. and Wilkinson, W. (1969) On branching processes in random environments. Ann. Math. Statist. 40, 814–827.Google Scholar
[10] Kaplan, N. (1970) Topics in the theory of branching processes with random environments. Unpublished thesis, Stanford University.Google Scholar