Discrete approximation of nonlinear filtering for stochastic delay equations

This paper deals with discrete–time approximation of nonlinear filtering problems in which both the state and observation processes are described by stochastic delay equations. The approach consists in approximating the original problem by Euler–type discrete–time model for which an optimal filter can be obtained by an explicit recursive procedure. The validity of the approach is substantiated by verifying the weak convergence of the approximating model to our original problem

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