Nonliner Filtering for Reflecting Diffusions in Random Enviroments via Nonparametric Estimation
Michael A. Kouritzin, University of Alberta, Canada
Wei Sun, University of Alberta and Concordia University, Canada
Jie Xiong, University of Tennessee
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.
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