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Wavelet-Galerkin method for the Kolmogorov equation
- Source :
-
Mathematical & Computer Modelling . Nov2004, Vol. 40 Issue 9/10, p1093-1121. 29p. - Publication Year :
- 2004
-
Abstract
- Abstract: 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. [Copyright &y& Elsevier]
- Subjects :
- *KOLMOGOROV complexity
*NUMERICAL analysis
*MACHINE theory
*MATHEMATICAL analysis
Subjects
Details
- Language :
- English
- ISSN :
- 08957177
- Volume :
- 40
- Issue :
- 9/10
- Database :
- Academic Search Index
- Journal :
- Mathematical & Computer Modelling
- Publication Type :
- Academic Journal
- Accession number :
- 17638488
- Full Text :
- https://doi.org/10.1016/j.mcm.2003.07.016