Superprocesses of stochastic flows

We construct a continuous superprocess X on M(Rd) which is the unique weak Feller extension of the empirical process of consistent k-point motions gen erated by a family of differential operators. The process X differs from kn own Dawson-Watanabe type, Fleming-Viot type and Ornstein-Uhlenbeck type sup erprocesses. This new type of superprocess provides a connection between st ochastic flows and measure-valued processes, and determines a stochastic co alescence which is similar to those of Smoluchowski. Moreover, the support of X describes how an initial measure on Rd is transported under the flow. As an example, the process realizes a viewpoint of Darling about the isotro pic stochastic flows under certain conditions.