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On a Continuous-State Population-Size-Dependent Branching Process and Its Extinction

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Yuqiang Li
Yuqiang Li*
Affiliation:
Beijing Normal University
*
∗ Postal address: School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China. Email address: y_q_li@163.com
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Abstract

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A continuous-state population-size-dependent branching process {Xt} is a modification of the Jiřina process. We prove that such a process arises as the limit of a sequence of suitably scaled population-size-dependent branching processes with discrete states. The extinction problem for the population Xt is discussed, and the limit distribution of Xt / t obtained when Xt tends to infinity.

Keywords

Population-size-dependent branching processfinite-dimensional distributionconvergenceextinctionlimit distribution

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J05: Discrete-time Markov processes on general state spaces

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 195 - 207
Copyright
© Applied Probability Trust 2006 

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