Nonlinear Filtering of Diffusion Processes in Correlated Noise: Analysis by Separation of Variables

Journal Article · Wed Mar 12 04:00:00 EST 2003 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-002-0760-4· OSTI ID:21064235

An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener chaos decomposition. The result is applied to the nonlinear filtering problem for the time-homogeneous diffusion model with correlated noise. An algorithm is proposed for computing recursive approximations of the unnormalized filtering density and filter, and the errors of the approximations are estimated. Unlike most existing algorithms for nonlinear filtering, the real-time part of the algorithm does not require solving partial differential equations or evaluating integrals. The algorithm can be used for both continuous and discrete time observations.

• OSTI ID: 21064235
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 47; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGORITHMS
APPROXIMATIONS
CHAOS THEORY
DIFFUSION
ERRORS
INTEGRALS
MATHEMATICAL SOLUTIONS
NOISE
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES