Asymptotic formulae for the optimal filtering error for finite state space Markov chains observed in independent noise are presented. Asymptotically optimal simple filters, which do not depend on the transition rates of the chain, are also presented.

This work is concerned with a class of semilinear stochastic functional parabolic differential equations of retarded type. We first establish conditions to ensure the existence of a unique non-negative solution of the stochastic delay partial differential equation under investigation....