Discrete time Galerkin approximations to the nonlinear filtering solution

AbstractThis paper concerns discrete time Galerkin approximations to the solution of the filtering problem for diffusions. Two families of schemes approximating the unnormalized conditional density, respectively, in an “average” and in a “pathwise” sense, are presented. L2 error estimates are derived and it is shown that the rate of convergence is linear in the time increment or linear in the modulus of continuity of the sample path