ON FILTERING EQUATIONS IN INFINITE DIMENSIONS

We consider a nonlinear filtering problem for a state process X in a H ilbert space H, given a finite dimensional observation process Y. We l ook for solutions of the corresponding filtering equations, having den sities with respect to a Gaussian reference measure in H. We derive th e equations for the conditional densities and prove that they have sol utions. We can allow correlated noise in the state and observation equ ations, provided additional assumptions hold. (C) 1997 academic Press