  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.
