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Displaying similar documents to “On the positivity and zero crossings of solutions of stochastic Volterra integrodifferential equations.”

Approximation of the Zakai equation in a nonlinear filtering problem with delay

Krystyna Twardowska, Tomasz Marnik, Monika Pasławska-Południak (2003)

International Journal of Applied Mathematics and Computer Science

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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.