Generalized white noise analysis and topological algebras

Daniel Alpay; Paula Cerejeiras; Uwe Kähler

doi:10.1080/17442508.2021.2016766

Generalized white noise analysis and topological algebras

Daniel Alpay, Paula Cerejeiras, Uwe Kähler

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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.

Original language	English
Journal	Stochastics
DOIs	https://doi.org/10.1080/17442508.2021.2016766
State	Accepted/In press - 1 Jan 2021
Externally published	Yes

Keywords

generalized fock space
grey noise space
Non-Gaussian analysis
strong algebras

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation

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10.1080/17442508.2021.2016766

Cite this

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title = "Generalized white noise analysis and topological algebras",

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-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 non-Gaussian stochastic processes.",

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N2 - 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.

AB - 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.

KW - generalized fock space

KW - grey noise space

KW - Non-Gaussian analysis

KW - strong algebras

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JO - Stochastics

JF - Stochastics

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Generalized white noise analysis and topological algebras

Abstract

Keywords

ASJC Scopus subject areas

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