An approximation for the Zakai equation

In this article we consider a polygonal approximation to the unnormalized c onditional measure of a filtering problem, which is the solution of the Zak ai stochastic differential equation on measure space. An estimate of the co nvergence rate based on a distance which is equivalent to the weak converge nce topology is derived. We also study the density of the unnormalized cond itional measure, which is the solution of the Zakai stochastic partial diff erential equation. An estimate of the convergence rate is also given in thi s case.