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March 2012 Extinction probability of interacting branching collision processes
Anyue Chen, Junping Li, Yiqing Chen, Dingxuan Zhou
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Adv. in Appl. Probab. 44(1): 226-259 (March 2012). DOI: 10.1239/aap/1331216651

Abstract

We consider the uniqueness and extinction properties of the interacting branching collision process (IBCP), which consists of two strongly interacting components: an ordinary Markov branching process and a collision branching process. We establish that there is a unique IBCP, and derive necessary and sufficient conditions for it to be nonexplosive that are easily checked. Explicit expressions are obtained for the extinction probabilities for both regular and irregular cases. The associated expected hitting times are also considered. Examples are provided to illustrate our results.

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Anyue Chen. Junping Li. Yiqing Chen. Dingxuan Zhou. "Extinction probability of interacting branching collision processes." Adv. in Appl. Probab. 44 (1) 226 - 259, March 2012. https://doi.org/10.1239/aap/1331216651

Information

Published: March 2012
First available in Project Euclid: 8 March 2012

zbMATH: 1260.60179
MathSciNet: MR2951553
Digital Object Identifier: 10.1239/aap/1331216651

Subjects:
Primary: 60J27
Secondary: 60J35

Keywords: collision branching process , extinction probability , extinction time , interaction , Markov branching process , regularity , uniqueness

Rights: Copyright © 2012 Applied Probability Trust

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Vol.44 • No. 1 • March 2012
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