<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

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

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

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

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

International Journal of Applied Mathematics and Computer Science

{"article-title":"On the convergence of the wavelet-Galerkin method for nonlinear filtering"}

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...

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

Published Online: Mar 25, 2010

Page range: 93 - 108

DOI: https://doi.org/10.2478/v10006-010-0007-5

Keywords
Zakai equation, Galerkin method, wavelet basis, Euler scheme

This content is open access.

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

Published Online: Mar 25, 2010

Page range: 93 - 108

DOI: https://doi.org/10.2478/v10006-010-0007-5

KeywordsZakai equation, Galerkin method, wavelet basis, Euler scheme

This content is open access.

Keywords
Zakai equation, Galerkin method, wavelet basis, Euler scheme