The reversibility and an SPDE for the generalized Fleming-Viot Processes   with mutation
  The (\Xi, 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 \Xi-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. 
Zenghu Li, Huili Liu, Jie Xiong, Xiaowen Zhou
math.PR