Probability-valued polynomial diffusions

We introduce polynomial diffusions taking values in the space of probability measures on a locally compact Polish space. We provide a representation of the corresponding extended generators, and prove well-posedness of the... [ view full abstract ]

We introduce polynomial diffusions taking values in the space of probability measures on a locally compact Polish space. 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.