On the convergence of the wavelet-Galerkin method for nonlinear filtering

• Autorzy: Łukasz D. Nowak , Monika Pasławska-Południak , Krystyna Twardowska
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Zakai equation; Galerkin method; wavelet basis; Euler scheme

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2010
• Tom: 20
• Numer: 1
• Strony: 93-108

Daty

wydano

2010

otrzymano

2008-11-14

poprawiono

2009-05-23

Twórcy

autor

Łukasz D. Nowak

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

autor

Monika Pasławska-Południak

• Department of Mathematics, Rzeszów University of Technology, ul. W. Pola 2, 35-959 Rzeszów, Poland

autor

Krystyna Twardowska

• Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences-SGGW, ul. Nowoursynowska 159, 02-776 Warsaw, Poland

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Identyfikatory

DOI

10.2478/v10006-010-0007-5