  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.
