Generalized white noise analysis and topological algebras. Issue 6 (18th August 2022)

• Record Type: Journal Article
• Authors: Alpay, Daniel; Cerejeiras, Paula; Kähler, Uwe
• Is Part Of: Stochastics. Volume 94:Issue 6(2022)
• Page Start: 926
• Page End: 958
• Publication Date: 2022-08-18
• Subjects: Non-Gaussian analysis -- grey noise space -- generalized fock space -- strong algebras; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2021.2016766
• Languages: English
• ISSNs: 1744-2508

Abstract

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.