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

Voir la notice de l'article provenant de la source Library of Science

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 
@article{IJAMCS_2003_13_2_a2,
     author = {Twardowska, K. and Marnik, T. and Pas{\l}awska-Po{\l}udniak, M.},
     title = {Approximation of the {Zakai} {Equation} in a {Nonlinear} {Filtering} {Problem} {With} {Delay}},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {151--160},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2003_13_2_a2/}
}
TY  - JOUR
AU  - Twardowska, K.
AU  - Marnik, T.
AU  - Pasławska-Południak, M.
TI  - Approximation of the Zakai Equation in a Nonlinear Filtering Problem With Delay
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2003
SP  - 151
EP  - 160
VL  - 13
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2003_13_2_a2/
LA  - en
ID  - IJAMCS_2003_13_2_a2
ER  - 
%0 Journal Article
%A Twardowska, K.
%A Marnik, T.
%A Pasławska-Południak, M.
%T Approximation of the Zakai Equation in a Nonlinear Filtering Problem With Delay
%J International Journal of Applied Mathematics and Computer Science
%D 2003
%P 151-160
%V 13
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2003_13_2_a2/
%G en
%F IJAMCS_2003_13_2_a2
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/