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The collision branching process

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Anyue Chen ,
Phil Pollett ,
Hanjun Zhang  and
Junping Li
Anyue Chen*
Affiliation:
University of Greenwich
Phil Pollett*
Affiliation:
University of Queensland
Hanjun Zhang*
Affiliation:
University of Queensland
Junping Li*
Affiliation:
University of Greenwich
*
∗ Postal address: School of Computing and Mathematical Science, University of Greenwich, 30 Park Row, Greenwich, London SE10 9LS, UK
∗∗∗ Postal address: Department of Mathematics, University of Queensland, QLD 4072, Australia.
∗∗∗ Postal address: Department of Mathematics, University of Queensland, QLD 4072, Australia.
∗ Postal address: School of Computing and Mathematical Science, University of Greenwich, 30 Park Row, Greenwich, London SE10 9LS, UK
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Abstract

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

Keywords

Regularityextinction probabilityhitting time

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1033 - 1048
Copyright
Copyright © Applied Probability Trust 2004 

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