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

Łukasz D. Nowak; Monika Pasławska-Południak; Krystyna Twardowska

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 1, page 93-108
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Łukasz D. Nowak, Monika Pasławska-Południak, and Krystyna Twardowska. "On the convergence of the wavelet-Galerkin method for nonlinear filtering." International Journal of Applied Mathematics and Computer Science 20.1 (2010): 93-108. <http://eudml.org/doc/207981>.

@article{ŁukaszD2010,
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.},
author = {Łukasz D. Nowak, Monika Pasławska-Południak, Krystyna Twardowska},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Zakai equation; Galerkin method; wavelet basis; Euler scheme},
language = {eng},
number = {1},
pages = {93-108},
title = {On the convergence of the wavelet-Galerkin method for nonlinear filtering},
url = {http://eudml.org/doc/207981},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Łukasz D. Nowak
AU - Monika Pasławska-Południak
AU - Krystyna Twardowska
TI - On the convergence of the wavelet-Galerkin method for nonlinear filtering
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 1
SP - 93
EP - 108
AB - 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.
LA - eng
KW - Zakai equation; Galerkin method; wavelet basis; Euler scheme
UR - http://eudml.org/doc/207981
ER -

References

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