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Extension of the Kalman-Bucy filter to elementary linear systems with fractional Brownian noises. (English) Zbl 1011.60018

The optimal filtering problem in the simplest Gaussian linear system driven by fractional Brownian motions is investigated. To this setting the Kalman-Bucy filtering equations are extended. Closed form Volterra type integral equations are derived both for the mean of the optimal filter and the variance of the filtering error. The asymptotic stability of the filter is analyzed. It is shown that the variance of the filtering error converges to a finite limit as the observation time tends to infinity.

MSC:

60G35 Signal detection and filtering (aspects of stochastic processes)
62M20 Inference from stochastic processes and prediction
93E11 Filtering in stochastic control theory
60G15 Gaussian processes
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