Geodesic
Approximation of the Zakai Equation in a Nonlinear Filtering Problem With Delay
International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) no. 2, pp. 151-160.

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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: stochastic differential equations with delay, Zakai's equation, nonlinear filtering
Mots-clés : matematyka 
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     title = {Approximation of the {Zakai} {Equation} in a {Nonlinear} {Filtering} {Problem} {With} {Delay}},
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Twardowska, K.; Marnik, T.; Pasławska-Południak, M. Approximation of the Zakai Equation in a Nonlinear Filtering Problem With Delay. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) no. 2, pp. 151-160. http://geodesic.mathdoc.fr/item/IJAMCS_2003_13_2_a2/