Generalized white noise analysis and topological algebras. Issue 6 (18th August 2022) - Alpay, Daniel; Cerejeiras, Paula; Kähler, Uwe
Abstract : 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-Itô 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 non-Gaussian stochastic processes.