Mckean-Vlasov Equations And Small Time Asymptotics For Fleming-Viot Processes

Fleming-Viot processes arising from population genetics are probability-valuedMarkov processes. As a class of fundamental measure-valued processes, it has beenstudied by many references.In section 2, the existence and uniqueness for a class of Mckean-Vlasov equatinsin the space of probabilities on a compact space is obtained by aprobabilistic ap-proach; the mentioned equations are of interests for Fleming-Viot processes.In section 3,small time asymptotics sample path large deviation for Fleming-Viot processes with selections is obtained; and the rate function is the energy func-tional of paths with respect to the intrinsic metric of Fleming-Viot processes.