A support theorem for the filter under infinite dimensional noise and unbounded observation coefficient

in Applied Mathematics & Optimization (1999), 39

In this paper we consider a nonlinear filtering problem with an unbounded observation coefficient, correlated noises, and a signal process driven by an infinite dimensional Brownian motion. We prove that ... [more ▼]

In this paper we consider a nonlinear filtering problem with an unbounded observation coefficient, correlated noises, and a signal process driven by an infinite dimensional Brownian motion. We prove that the unnormalized filter admits a smooth density which is in the Schwartz space and we give a description of the support of the law of this density. [less ▲]