Kolmogorov equations on spaces of measures associated to nonlinear filtering processes

We introduce and study some backward Kolmogorov equations associated to filtering problems. In the stochastic framework, SDEs for measure-valued processes arise naturally (Zakai Kushner–Stratonovich equation). The have been intensively studies, assuming that admit a density then by exploiting calculus in Hilbert spaces. Our approach differs from this since we do not assume existence of work directly context measures. first formulate two on spaces measures, prove uniqueness classical solutions.