New Method for optimal nonlinear filtering of noisy observations by multiple stochastic fractional integral expansions
✍ Scribed by A. Amirdjanova; S. Chivoret
- Book ID
- 104007868
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 902 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
Multiple stochastic fractional integral expansions are applied to the problem of nonlinear 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 meansquare estimate of the signal can be represented as a ratio of two multiple integral series, where the stochastic integrals are defined in either the It6 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.