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In this paper we introduce a new approach to the study of filtering theory byallowing the system's parameters to have a random character. We use Hida'swhite noise space theory to give an alternative characterization and a propergeneralization to the Wiener filter over a suitable space of stochasticdistributions introduced by Kondratiev. The main idea throughout this paper isto use the nuclearity of this spaces in order to view the random variables asbounded multiplication operators (with respect to the Wick product) betweenHilbert spaces of stochastic distributions. This allows us to use operatortheory tools and properties of Wiener algebras over Banach spaces to proceedand characterize the Wiener filter equations under the underlying randomnessassumptions.

Stochastic Wiener Filter in the White Noise Space