Nonlinear Filtering for Reflecting Diffusions in Random Enviroments via Nonparametric Estimation

Abstract

We study a nonlinear filtering problem in which the signal to be estimated is a reflecting diffusion in a random environment. Under the assumption that the observation noise is independent of the signal, we develop a nonparametric functional estimation method for finding workable approximate solutions to the conditional distributions of the signal state. Furthermore, we show that the pathwise average distance, per unit time, of the approximate filter from the optimal filter is asymptotically small in time. Also, we use simulations based upon a particle filter algorithm to show the efficiency of the method.