  In this paper we introduce a new approach to the study of filtering theory by
allowing the system's parameters to have a random character. We use Hida's
white noise space theory to give an alternative characterization and a proper
generalization to the Wiener filter over a suitable space of stochastic
distributions introduced by Kondratiev. The main idea throughout this paper is
to use the nuclearity of this spaces in order to view the random variables as
bounded multiplication operators (with respect to the Wick product) between
Hilbert spaces of stochastic distributions. This allows us to use operator
theory tools and properties of Wiener algebras over Banach spaces to proceed
and characterize the Wiener filter equations under the underlying randomness
assumptions.
