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

100%

Twardowska K., Marnik T., Pasławska-Południak M.

International Journal of Applied Mathematics and Computer Science

2003

tom 13

nr 2

151-160

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.

Nonlinear filtering for Markov systems with delayed observations

88%

Calzolari A., Florchinger P., Nappo G.

International Journal of Applied Mathematics and Computer Science

2009

tom 19

nr 1

49-57

This paper deals with nonlinear filtering problems with delays, i.e., we consider a system (X,Y), which can be represented by means of a system (X,Ŷ), in the sense that Yt = Ŷa(t), where a(t) is a delayed time transformation. We start with X being a Markov process, and then study Markovian systems, not necessarily diffusive, with correlated noises. The interest is focused on the existence of explicit representations of the corresponding filters as functionals depending on the observed trajectory. Various assumptions on the function a(t) are considered.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Calzolari A.

1 Florchinger P.

1 Marnik T.

1 Nappo G.

1 Pasławska-Południak M.

1 Twardowska K.

1 2009

1 2003

Wyniki wyszukiwania

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

Nonlinear filtering for Markov systems with delayed observations