An approximate McKean-Vlasov model for the stochastic filtering problem

Abstract

The solution of the stochastic filtering problem is approximated using Clark's robust representation approach [ Proc. 2nd NATO Advanced Study Inst. , Darlington, 1977, pp. 721–734]. 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 [ Stochastic Process. Appl. 86 (2000), no. 2, 193–216.] in the context of Feynman-Kac formulae. The representation introduced below differs from the one introduced in [Del Moral and Miclo, Stochastic Process. Appl. 86 (2000), no. 2, 193–216.] as it involves processes with no jumps.