The reversibility and an SPDE for the generalized Fleming–Viot processes with mutation

Zenghu Li, Huili Liu, Jie Xiong and Xiaowen Zhou

Stochastic Processes and their Applications, 2013, vol. 123, issue 12, 4129-4155

Abstract: The (Ξ,A)-Fleming–Viot process with mutation is a probability-measure-valued process whose moment dual is similar to that of the classical Fleming–Viot process except that Kingman’s coalescent is replaced by the Ξ-coalescent, the coalescent with simultaneous multiple collisions. We first prove the existence of such a process for general mutation generator A. We then investigate its reversibility. We also study both the weak and strong uniqueness of the solution to the associated stochastic partial differential equation.

Keywords: Fleming–Viot process; Reversibility; Ξ-coalescent; Stochastic partial differential equation; Strong uniqueness (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:12:p:4129-4155

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DOI: 10.1016/j.spa.2013.06.013

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