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.
@article{bwmeta1.element.bwnjournal-article-amcv13i2p151bwm,
author = {Twardowska, Krystyna and Marnik, Tomasz and Pas\l awska-Po\l udniak, Monika},
title = {Approximation of the Zakai equation in a nonlinear filtering problem with delay},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {13},
year = {2003},
pages = {151-160},
zbl = {1052.93058},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv13i2p151bwm}
}
Twardowska, Krystyna; Marnik, Tomasz; Pasławska-Południak, Monika. Approximation of the Zakai equation in a nonlinear filtering problem with delay. International Journal of Applied Mathematics and Computer Science, Tome 13 (2003) pp. 151-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv13i2p151bwm/
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