In this paper we develop a framework to extend the theory of generalized stochastic processes in the Hida white noise space to more general probability spaces which include the grey noise space. To obtain a Wiener-It^o expansion we recast it as a moment problem and calculate the moments explicitly. We further show the importance of a family of topological algebras called strong algebras in this context. Furthermore we show the applicability of our approach to the study of stochastic processes.
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