Interacting Fleming-Viot processes

Jean Vaillancourt

Stochastic Processes and their Applications, 1990, vol. 36, issue 1, 45-57

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.

Keywords: Fleming-Viot; process; measure-valued; processes; duality; scaling; theorem; martingale; problems (search for similar items in EconPapers)
Date: 1990
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