An approximate McKean-Vlasov model for the stochastic filtering problem

Abstract

Abstract. The solution of the stochastic filtering problem is approximated using Clark's robust representation approach [1]. The ensuing approximation is shown to coincide with the time marginals of solutions of a certain McKean-Vlasov type process. The result leads to a representation of the solution of the stochastic filtering problem as a limit of empirical distributions of systems of equally weighted particles. A similar representation has been introduced by Del Moral and Miclo in [9] in the context of Feynman-Kac formulae. The representation introduced below differs from the one introduced in [9] as it involves processes with no jumps.