Immortal particle for a catalytic branching process |
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Authors: | Ilie Grigorescu Min Kang |
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Affiliation: | 1. Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL, 33124-4250, USA 2. Department of Mathematics, North Carolina State University, SAS Hall, 2311 Stinson Dr., Box 8205, Raleigh, NC, 27695, USA
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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. |
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