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Two-Sex Branching Processes with Offspring and Mating in a Random Environment

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

S. Ma  and
M. Molina
S. Ma*
Affiliation:
Hebei University of Technology
M. Molina*
Affiliation:
University of Extremadura
*
∗Postal address: Department of Applied Mathematics, Hebei University of Technology, Tianjin, China. Email address: mashixia1@163.com
∗∗Postal address: Department of Mathematics, University of Extremadura, 06071 Badajoz, Spain. Email address: mmolina@unex.es
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Abstract

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We introduce a class of discrete-time two-sex branching processes where the offspring probability distribution and the mating function are governed by an environmental process. It is assumed that the environmental process is formed by independent but not necessarily identically distributed random vectors. For such a class, we determine some relationships among the probability generating functions involved in the mathematical model and derive expressions for the main moments. Also, by considering different probabilistic approaches we establish several results concerning the extinction probability. A simulated example is presented as an illustration.

Keywords

Branching processtwo-sex processrandom environment processextinction probability

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 46 , Issue 4 , December 2009 , pp. 993 - 1004
Copyright
Copyright © Applied Probability Trust 2009 

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