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.


Full Text : http://www.dtic.mil/get-tr-doc/pdf?AD=ADA202519


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