Advances in Applied Probability

Extinction probability of interacting branching collision processes

Anyue Chen, Junping Li, Yiqing Chen, and Dingxuan Zhou

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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.

Article information

Source
Adv. in Appl. Probab., Volume 44, Number 1 (2012), 226-259.

Dates
First available in Project Euclid: 8 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1331216651

Digital Object Identifier
doi:10.1239/aap/1331216651

Mathematical Reviews number (MathSciNet)
MR2951553

Zentralblatt MATH identifier
1260.60179

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

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

Citation

Chen, Anyue; Li, Junping; Chen, Yiqing; Zhou, Dingxuan. Extinction probability of interacting branching collision processes. Adv. in Appl. Probab. 44 (2012), no. 1, 226--259. doi:10.1239/aap/1331216651. https://projecteuclid.org/euclid.aap/1331216651


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