Document Zbl 1251.60064

Immortal particle for a catalytic branching process. (English) Zbl 1251.60064

Probab. Theory Relat. Fields 153, No. 1-2, 333-361 (2012).

Authors’ abstract: We study the existence and asymptotic properties of a conservative branching particle system driven by a diffusion with smooth coefficients for which birth and death are triggered by contact with a set. Sufficient conditions for the process to be non-explosive are given. In the Brownian motions case the domain of evolution can be non-smooth, including Lipschitz, with integrable Martin kernel. The results are valid for an arbitrary number of particles and non-uniform redistribution after branching. Additionally, with probability one, it is shown that only one ancestry line survives. In special cases, the evolution of the surviving particle is studied, and, for a two particle system on a half line, we derive explicitly the transition function of a chain representing the position at successive branching times.

Reviewer: P. R. Parthasarathy (Chennai)

Cited in 17 Documents

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60J35	Transition functions, generators and resolvents
60J75	Jump processes (MSC2010)

Keywords:

Fleming-Viot branching; immortal particle; Martin kernel; Doeblin condition; jump diffusion process

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References:

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