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Paper details
Number 1 - March 2010
Volume 20 - 2010
On the convergence of the wavelet-Galerkin method for nonlinear filtering
Łukasz D. Nowak, Monika Pasławska-Południak, Krystyna Twardowska
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.
Keywords
Zakai equation, Galerkin method, wavelet basis, Euler scheme