PDE, Differential Geometric, Algebraic, Wavelet and Parallel Computation Methods in Nonlinear Filtering

摘要

It is well known that the Yau filter is the most general finite dimensional filter. The principal investigator and Dr. G.Q. Hu were able to construct the finite dimensional Yau filter by solving a Kolmogorov equation that is independent of observations and a system of 1st order linear ODEs that depends on observations. The principal investigator and S.T. Yau gave an affirmative answer to the main problem in nonlinear filtering theory. They answered the challenge proposed by the Naval Research Office a few years ago: how can one solve the nonlinear filtering problem if an adequate amount of computational resources is provided. This report contains a list of 27 papers and technical reports written by the author, a list of all scientific personnel who participated in the research, and a curriculum vitae for Stephen Shing-Toung Yau that includes professional activities and a list of 213 publications. (33 refs.).