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

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

Publishing date

2002-10-04

URL

arxiv.org/abs/math/0210068v1

Science

Mathematics

Field

Probability

Type

Scientific paper

Abstract

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.

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