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Quasi-invariance and reversibility in the Fleming–Viot process

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Abstract

 Fleming–Viot processes with mutation, selection and recombination are studied. Their reversible distributions are shown to be characterized as quasi-invariant measures with a cocycle given in terms of the mutation operator, the selection intensity, and the recombination kernel. By using this, we derive not only a necessary and sufficient condition for the Fleming–Viot process to be reversible, but also identify the reversible distributions in the reversible case.

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Received: 18 January 2001 / Revised version: 21 June 2001 / Published online: 22 February 2002

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Handa, K. Quasi-invariance and reversibility in the Fleming–Viot process. Probab Theory Relat Fields 122, 545–566 (2002). https://doi.org/10.1007/s004400100178

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Keywords

  • Recombination
  • Mutation Operator
  • Reversible Case
  • Selection Intensity
  • Reversible Distribution