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

Krystyna Twardowska; Tomasz Marnik; Monika Pasławska-Południak

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 2, page 151-160
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Twardowska, Krystyna, Marnik, Tomasz, and Pasławska-Południak, Monika. "Approximation of the Zakai equation in a nonlinear filtering problem with delay." International Journal of Applied Mathematics and Computer Science 13.2 (2003): 151-160. <http://eudml.org/doc/207630>.

@article{Twardowska2003,
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.},
author = {Twardowska, Krystyna, Marnik, Tomasz, Pasławska-Południak, Monika},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {stochastic differential equations with delay; Zakai's equation; nonlinear filtering; Galerkin technique},
language = {eng},
number = {2},
pages = {151-160},
title = {Approximation of the Zakai equation in a nonlinear filtering problem with delay},
url = {http://eudml.org/doc/207630},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Twardowska, Krystyna
AU - Marnik, Tomasz
AU - Pasławska-Południak, Monika
TI - Approximation of the Zakai equation in a nonlinear filtering problem with delay
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 2
SP - 151
EP - 160
AB - 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.
LA - eng
KW - stochastic differential equations with delay; Zakai's equation; nonlinear filtering; Galerkin technique
UR - http://eudml.org/doc/207630
ER -

References

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