Accession Number : ADA202519
Title : Nonlinear Filtering and Approximation Techniques
Descriptive Note : Final rept.
Corporate Author : INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE ROCQUENCOURT (FRANCE)
Personal Author(s) : Pardoux, E
Report Date : Oct 1988
Pagination or Media Count : 166
Abstract : This research concerned the theory of nonlinear filtering and numerical approximation in nonlinear filtering. The following results were obtained: 1) Under very general conditions it is shown that the conditional density in nonlinear filtering is the unique solution, within an appropriate class of functions, of the Zakai equation. The main conditions is that all coefficients are bounded and smooth. These coefficients are allowed to depend on the history of the observed process; 2) Developed a Lie algebraic criterion for the non-existence of finite dimensional filters; 3) Studied numerical methods for the approximate solution of Zakai's stochastic partial differential equations; 4) Developed approximate finite dimensional filters for high signal to noise ratio problems; and 5) Compared two algorithms for maximizing the likelihood function associated with parameter estimation in partially observed diffusion processes.
Descriptors : *MATHEMATICAL FILTERS , *APPROXIMATION(MATHEMATICS) , *DETECTORS , STOCHASTIC PROCESSES , SIZES(DIMENSIONS) , PARAMETERS , THEORY , ESTIMATES , NONLINEAR SYSTEMS , COEFFICIENTS , SIGNALS , PARTIAL DIFFERENTIAL EQUATIONS , DIFFUSION , FILTERS , NOISE , NUMERICAL METHODS AND PROCEDURES , RATIOS , EQUATIONS , ALGORITHMS , FUNCTIONS
Subject Categories : Numerical Mathematics
Miscellaneous Detection and Detectors
Distribution Statement : APPROVED FOR PUBLIC RELEASE