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
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
收藏
页码:1093 / 1121
页数:29
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