Abstract

In this paper we prove exponential asymptotic stability for discrete time filters for signals arising as solutions of d-dimensional stochastic difference equations. The observation process is the signal corrupted by an additive white noise of su#ciently small variance. The model for the signal admits non-ergodic processes. We show that almost surely, the total variation distance between the optimal filter and an incorrectly initialized filter converges to 0 exponentially fast as time approaches #. Key Words: nonlinear filtering, asymptotic stability, measure valued processes. # Research suppored by the NSF grant DMI 9812857. 1 1 Introduction The central problem of nonlinear filtering is to study the conditional distribution of a signal process at any time instant given noisy observations on the signal available up until that time. If the signal--observation pair is Markov, the conditional distribution process, referred to hereafter as the optimal filter , is determined completely ...

Citations