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Paper details
Number 2 - June 2003
Volume 13 - 2003
Approximation of the Zakai equation in a nonlinear filtering problem with delay
Krystyna Twardowska, Tomasz Marnik, Monika Pasławska-Południak
Abstract
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