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Branching processes with deteriorating random environments

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Peter Jagers  and
Zhunwei Lu
Peter Jagers*
Affiliation:
Chalmers University of Technology and Göteborg University
Zhunwei Lu*
Affiliation:
Taiyuan University of Technology
*
∗ Postal address: Department of Mathematical Statistics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden. Email address: jagers@math.chalmers.se
∗∗ Postal address: Department of Mathematics, Taiyuan University of Technology, 030024, Taiyuan, Shanxi Province, China.
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Abstract

We introduce Galton-Watson-style branching processes in random environments which are deteriorating rather than stationary or independent. Some primary results on process growth and extinction probability are shown, and two simple examples are given.

Keywords

Branching processrandom environmentpopulation growth

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K37: Processes in random environments
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 2 , June 2002 , pp. 395 - 401
Copyright
Copyright © Applied Probability Trust 2002 

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References

[1] Athreya, K. B., and Karlin, S. (1971). On branching processes with random environments, I: extinction probabilities. Ann. Math. Statist. 42, 1499–1520.Google Scholar
[2] Jagers, P. (1992). Stabilities and instabilities in population dynamics. J. Appl. Prob. 29, 770–780.Google Scholar
[3] Klebaner, F. C. (1984). On population-size-dependent branching processes. Adv. Appl. Prob. 16, 30–55.CrossRefGoogle Scholar
[4] Smith, W. L., and Wilkinson, W. E. (1969). On branching processes in random environments. Ann. Math. Statist. 40, 814–827.Google Scholar
[5] Wang, H. (1999). Extinction of population-size-dependent branching processes in random environments. J. Appl. Prob. 36, 146–154.Google Scholar