Optimal Control and Nonlinear Filtering for Nondegenerate Diffusion Processes

Abstract

A linear parabolic partial differential equation describing the pathwise filter for a nondegenerate diffusion is changed, by an exponential substitution. into the dynamic programming equation of an optimal stochastic control problem. This substitution is applied to obtain results about the rate of decay as of solutions p(x,t)to the pathwise filter equation, and for solutions of the corresponding Zakai equation