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The distribution of the spine of a Fleming–Viot type process

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  • Bieniek, Mariusz
  • Burdzy, Krzysztof

Abstract

We show uniqueness of the spine of a Fleming–Viot particle system under minimal assumptions on the driving process. If the driving process is a continuous time Markov process on a finite space, we show that asymptotically, when the number of particles goes to infinity, the distribution of the spine converges to that of the driving process conditioned to stay alive forever, the branching rate for the spine is twice that of a generic particle in the system, and every side branch has the distribution of the unconditioned generic branching tree.

Suggested Citation

  • Bieniek, Mariusz & Burdzy, Krzysztof, 2018. "The distribution of the spine of a Fleming–Viot type process," Stochastic Processes and their Applications, Elsevier, vol. 128(11), pages 3751-3777.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:11:p:3751-3777
    DOI: 10.1016/j.spa.2017.12.003
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    Keywords

    Fleming–Viot particle system; Spine;

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