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Immortal particle for a catalytic branching process
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  • Published: 22 February 2011

Immortal particle for a catalytic branching process

  • Ilie Grigorescu1 &
  • Min Kang2 

Probability Theory and Related Fields volume 153, pages 333–361 (2012)Cite this article

  • 225 Accesses

  • 19 Citations

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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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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Miami, 1365 Memorial Drive, Coral Gables, FL, 33124-4250, USA

    Ilie Grigorescu

  2. Department of Mathematics, North Carolina State University, SAS Hall, 2311 Stinson Dr., Box 8205, Raleigh, NC, 27695, USA

    Min Kang

Authors
  1. Ilie Grigorescu
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  2. Min Kang
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Corresponding author

Correspondence to Ilie Grigorescu.

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Cite this article

Grigorescu, I., Kang, M. Immortal particle for a catalytic branching process. Probab. Theory Relat. Fields 153, 333–361 (2012). https://doi.org/10.1007/s00440-011-0347-6

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  • Received: 05 June 2009

  • Revised: 27 December 2010

  • Published: 22 February 2011

  • Issue Date: June 2012

  • DOI: https://doi.org/10.1007/s00440-011-0347-6

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Keywords

  • Fleming–Viot branching
  • Immortal particle
  • Martin kernel
  • Doeblin condition
  • Jump diffusion process

Mathematics Subject Classification (2000)

  • Primary 60J35
  • Secondary 60J75
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