Lectures on linear and nonlinear filtering
on Analysis and estimation of stochastic mechanical systems
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
An introduction to wavelets
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
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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.