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

Authors:
ŁUkasz Nowak;Monika PasłAwska-PołUdniak;Krystyna Twardowska
Affiliations:
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
Venue:
International Journal of Applied Mathematics and Computer Science - Computational Intelligence in Modern Control Systems
Year:
2010

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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.