We introduce polynomial diffusions taking values in the space of probability mea-
sures on a locally compact Polish space, generalizing the well-known Fleming-Viot process.
We provide a representation of the corresponding extended generators, and prove well-
posedness of the associated martingale problems. In particular, we obtain uniqueness
by establishing a formula for the conditional moments of the solution, which in the
finite-dimensional case reduces to a matrix exponential.
The talk is based on joint work with Martin Larsson and Sara Svaluto Ferro.

Scientific Committee