STOCHASTIC PARTIAL-DIFFERENTIAL EQUATIONS ON MANIFOLDS .2. NONLINEAR FILTERING

The conditional law of an unobservable component x(t) of a diffusion ( x(t), y(t)) given the observations {y(s): s is an element of [0, t]} i s investigated when x(t) lives on a submanifold M of R(n). The existen ce of the conditional density with respect to a given measure on M is shown under fairly general conditions, and the analytical properties o f this density are characterized in terms of the Sobolev spaces used i n the first part of this series.