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

2012/10/11 by Zenghu Li, Li, Zenghu, Huili Liu +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · #60H15 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Primary 60G57 #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #secondary 60J80

paper · pdf · doi:10.48550/arxiv.1210.3259

openalex publication_date 2012/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks

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