Approximation of the Zakai equation in a nonlinear filtering problem with delay - Twardowska, Krystyna; Marnik, Tomasz; Pasławska-Południak, Monika (Zielona Góra: Uniwersytet Zielonogórski)
A nonlinear filtering problem with delays in the state and observation equations is considered. The unnormalized conditional probability density of the filtered diffusion process satisfies the so-called Zakai equation and solves the nonlinear filtering problem. We examine the solution of the Zakai equation using an approximation result. Our theoretical deliberations are illustrated by a numerical example.
Keywords: nonlinear filtering; stochastic differential equations with delay; Zakai's equation