New Method for optimal nonlinear filtering of noisy observations by multiple stochastic fractional integral expansions

Authors:
A. Amirdjanova;S. Chivoret
Affiliations:
Department of Statistics, The University of Michigan 439 West Hall, 1085 S. University Ave. Ann Arbor, MI 48109-1107, U.S.A.;Department of Mathematics, The University of Michigan 530 Church St., Ann Arbor, MI 48109, U.S.A.
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 2
Cited 1

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SIAM Journal on Control and Optimization
Stochastic Calculus for Fractional Brownian Motion I. Theory

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Stochastic evolution equations for nonlinear filtering of random fields in the presence of fractional Brownian sheet observation noise

Computers & Mathematics with Applications

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Abstract

Multiple stochastic fractional integral expansions are applied to the problem of non-linear filtering of a signal observed in the presence of an additive noise, where the noise is modelled by a fractional Brownian motion with Hurst index greater than 1/2. It is shown that the best mean-square estimate of the signal can be represented as a ratio of two multiple integral series, where the stochastic integrals are defined in either the Ito or Stratonovich sense and taken with respect to the observation process, which is a persistent fractional Brownian motion under a suitable probability measure. Finally, motivated by practical considerations, finite expansion approximations to the optimal filter are studied.