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On the differential equation satisfied by the random measure density of a jump-type Fleming–Viot process

The subject matter of this paper is the so-called jump-type Fleming–Viot process. The main result shows that the density of the process has a representation as the solution of a stochastic partial differential equation. When reduced to the Fleming–Viot process, our result recovers the result of N. Konno and T. Shiga [Stochastic partial differential equations for some measure-valued diffusions, Probab. Theory Relat. Fields 79 (1988), pp. 201–225].