Generalized Fock space and moments

2020/05/16 by Daniel Alpay, Alpay, Daniel, Paula Cerejeiras +3
Economics, Econometrics and Finance · Mathematics · #33E12 #46F25 #60G22 #60H40 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2005.08085

openalex publication_date 2020/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 stochastic processes.

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