Extinction probability of interacting branching collision processes

Anyue Chen; Junping Li; Yiqing Chen; Dingxuan Zhou

doi:10.1239/aap/1331216651

Extinction probability of interacting branching collision processes

Anyue Chen^*, Junping Li, Yiqing Chen, Dingxuan Zhou

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

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.

Original language	English
Pages (from-to)	226-259
Number of pages	34
Journal	Advances in Applied Probability
Volume	44
Issue number	1
DOIs	https://doi.org/10.1239/aap/1331216651
Publication status	Published - Mar 2012
Externally published	Yes

Keywords

Collision branching process
Extinction probability
Extinction time
Interaction
Markov branching process
Regularity
Uniqueness

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AU - Li, Junping

AU - Chen, Yiqing

AU - Zhou, Dingxuan

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N2 - 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.

AB - 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.

KW - Collision branching process

KW - Extinction probability

KW - Extinction time

KW - Interaction

KW - Markov branching process

KW - Regularity

KW - Uniqueness

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JO - Advances in Applied Probability

JF - Advances in Applied Probability

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Extinction probability of interacting branching collision processes

Abstract

Keywords

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