Wavelet-Galerkin method for the Kolmogorov equation

被引：3

作者：

Liang, ZG ^{[1
]}

Yau, SST ^{[1
]}

机构：

[1] Univ Illinois, Dept MSCS, Chicago, IL 60607 USA

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2004年 / 40卷 / 9-10期

关键词：

nonlinear filtering; Kolmogorov equation; Wavelet-Galerkin method; Daubechies scaling function; pyramid algorithm;

D O I：

10.1016/j.mcm.2003.07.016

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

It is well known that the Kolmogorov equation plays an important role in applied science. For example, the nonlinear filtering problem, which plays a key role in modern technologies, was solved by Yau and Yau [1] by reducing it to the off-line computation of the Kolmogorov equation. In this paper, we develop a theorical foundation of using the wavelet-Galerkin method to solve linear parabolic P.D.E. We apply our theory to the Kolmogorov equation. We give a rigorous proof that the solution of the Kolmogorov equation can be approximated very well in any finite domain by our wavelet-Galerkin method. An example is provided by using Daubechies D-4 scaling functions. (C) 2004 Elsevier Ltd. All rights reserved.

引用

页码：1093 / 1121

页数：29

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