Temat: Zakai's equation - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Approximation of the Zakai Equation in a Nonlinear Filtering Problem With Delay
Autorzy:: Twardowska, K.
Marnik, T.
Pasławska-Południak, M.
Powiązania:: https://bibliotekanauki.pl/articles/908197.pdf
Data publikacji:: 2003
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: stochastic differential equations with delay
Zakai's equation
nonlinear filtering
matematyka
Opis:: 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.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2003, 13, 2; 151-160
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: A relaxation theorem for partially observed stochastic control on Hilbert space
Autorzy:: Ahmed, N.
Powiązania:: https://bibliotekanauki.pl/articles/729417.pdf
Data publikacji:: 2007
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: partially observed control
infinite dimensional Hilbert space
relaxed controls
Zakai equation
Opis:: In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that the set of solutions corresponding to ordinary controls is weakly dense in the set of solutions corresponding to relaxed controls. This is presented in Theorem 5.3 after giving some existence results on optimal controls for the infinite dimensional Zakai equation used for its proof.
Źródło:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 295-314
1509-9407
Pojawia się w:: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On the convergence of the wavelet-Galerkin method for nonlinear filtering
Autorzy:: Nowak, Ł. D.
Pasławska-Południak, M.
Twardowska, K.
Powiązania:: https://bibliotekanauki.pl/articles/907779.pdf
Data publikacji:: 2010
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: równanie Zakai
metoda Galerkina
falka
schemat Eulera
Zakai equation
Galerkin method
wavelet basis
Euler scheme
Opis:: The aim of the paper is to examine the wavelet-Galerkin method for the solution of filtering equations. We use a wavelet biorthogonal basis with compact support for approximations of the solution. Then we compute the Zakai equation for our filtering problem and consider the implicit Euler scheme in time and the Galerkin scheme in space for the solution of the Zakai equation. We give theorems on convergence and its rate. The method is numerically much more efficient than the classical Galerkin method.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2010, 20, 1; 93-108
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
Dostawca treści:: Biblioteka Nauki

Artykuł

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