SPD

Abstract

We give an overview on results on stability of the optimal filter for signal processes with state space $\mathbb{R}^d$ observed with independent additive noise, both in discrete and continuous time. Explicit lower bounds on the rate of stability in terms of the coefficients of the signal and the observation are obtained. For the time-continuous case the bounds are uniform w.r.t. appropriate time-discrete approximations. I also discuss a particular extension to signals observed with independent multiplicative noise.