## Advances in Applied Probability

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

### Extinction probability of interacting branching collision processes

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

#### 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