ON THE CONVERGENCE OF THE WAVELET-GALERKIN METHOD FOR NONLINEAR FILTERING

被引：2

作者：

Nowak, Lukasz D. ^{[1
]}

Paslawska-Poludniak, Monika ^{[2
]}

Twardowska, Krystyna ^{[3
]}

机构：

[1] Warsaw Univ Technol, Fac Math & Informat Sci, PL-00661 Warsaw, Poland

[2] Rzeszow Univ Technol, Dept Math, PL-35959 Rzeszow, Poland

[3] Warsaw Univ Life Sci SGGW, Fac Appl Informat & Math, PL-02776 Warsaw, Poland

来源：

INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE | 2010年 / 20卷 / 01期

关键词：

Zakai equation; Galerkin method; wavelet basis; Euler scheme; REAL-TIME SOLUTION; ZAKAI EQUATION; APPROXIMATIONS; BASES;

D O I：

10.2478/v10006-010-0007-5

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：93 / 108

页数：16

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