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

Author

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  • Li, Zenghu
  • Liu, Huili
  • Xiong, Jie
  • Zhou, Xiaowen

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.

Suggested Citation

  • Li, Zenghu & Liu, Huili & Xiong, Jie & Zhou, Xiaowen, 2013. "The reversibility and an SPDE for the generalized Fleming–Viot processes with mutation," Stochastic Processes and their Applications, Elsevier, vol. 123(12), pages 4129-4155.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:12:p:4129-4155
    DOI: 10.1016/j.spa.2013.06.013
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    Cited by:

    1. He, Hui & Li, Zenghu & Yang, Xu, 2014. "Stochastic equations of super-Lévy processes with general branching mechanism," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1519-1565.

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