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arXiv · 1210.3259

The reversibility and an SPDE for the generalized Fleming-Viot Processes with mutation

Zenghu Li·Huili Liu·Jie Xiong·Xiaowen Zhou
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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 the 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 solution to the associated stochastic partial differential equation.

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Zenghu Li, Huili Liu, Jie Xiong, Xiaowen Zhou. 2012-10-11. The reversibility and an SPDE for the generalized Fleming-Viot Processes with mutation. https://arxiv.org/abs/1210.3259

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