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Interacting Fleming-Viot processes

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  • Vaillancourt, Jean

Abstract

We construct a class of interacting Ohta-Kimura stepwise-mutation models and study their macroscopic behavior, i.e., we prove their weak convergence when the population size n increases to infinity, the evolution is speeded up by a factor n2, the increment effects of a change in each population's distribution of characteristics under study is scaled down by a factor n and the level of interaction between populations is decreased by a factor n-1. The measure-valued limits--interacting Fleming-Viot processes--are characterized as unique solutions to certain martingale problems using the method of duality. Finally, we prove a scaling theorem for these processes.

Suggested Citation

  • Vaillancourt, Jean, 1990. "Interacting Fleming-Viot processes," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 45-57, October.
    • Handle: RePEc:eee:spapps:v:36:y:1990:i:1:p:45-57
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    Cited by:

    1. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.
    2. Christa Cuchiero & Martin Larsson & Sara Svaluto-Ferro, 2018. "Probability measure-valued polynomial diffusions," Papers 1807.03229, arXiv.org.

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