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Non-extinction of a Fleming-Viot particle model
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  • Published: 07 June 2011

Non-extinction of a Fleming-Viot particle model

  • Mariusz Bieniek1,
  • Krzysztof Burdzy2 &
  • Sam Finch3 

Probability Theory and Related Fields volume 153, pages 293–332 (2012)Cite this article

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  • 17 Citations

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Abstract

We consider a branching particle model in which particles move inside a Euclidean domain according to the following rules. The particles move as independent Brownian motions until one of them hits the boundary. This particle is killed but another randomly chosen particle branches into two particles, to keep the population size constant. We prove that the particle population does not approach the boundary simultaneously in a finite time in some Lipschitz domains. This is used to prove a limit theorem for the empirical distribution of the particle family.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Maria Curie Skłodowska University, pl. M. Curie-Skłodowskiej 1, 20-031, Lublin, Poland

    Mariusz Bieniek

  2. Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195, USA

    Krzysztof Burdzy

  3. BiRC, Aarhus University, Building 1110, C.F. Møller’s Alle 8, 8000, Aarhus C, Denmark

    Sam Finch

Authors
  1. Mariusz Bieniek
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  2. Krzysztof Burdzy
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  3. Sam Finch
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Corresponding author

Correspondence to Krzysztof Burdzy.

Additional information

Research supported in part by NSF Grant DMS-0906743 and by Grant N N201 397137, MNiSW, Poland.

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Cite this article

Bieniek, M., Burdzy, K. & Finch, S. Non-extinction of a Fleming-Viot particle model. Probab. Theory Relat. Fields 153, 293–332 (2012). https://doi.org/10.1007/s00440-011-0372-5

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  • Received: 13 May 2009

  • Revised: 14 May 2011

  • Published: 07 June 2011

  • Issue Date: June 2012

  • DOI: https://doi.org/10.1007/s00440-011-0372-5

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Keywords

  • Brownian motion
  • Branching particle system

Mathematics Subject Classification (2000)

  • 60J65
  • 60J80
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