@article{3e32da9ac52f41c2a472bdb7ac71ca61,
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.",
keywords = "Non-Gaussian analysis, generalized fock space, grey noise space, strong algebras",
author = "Daniel Alpay and Paula Cerejeiras and Uwe K{\"a}hler",
note = "Funding Information: The first author thanks the Foster G. and Mary McGaw Professorship in Mathematical Sciences, which supported this research. The second author wishes to thank also the support of the Portuguese Foundation for Science and Technology under the FCT Sabbatical grant. Funding Information: The work of the second and third authors was supported by Portuguese funds through the CIDMA–Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology ({\textquoteleft}FCT–Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia{\textquoteright}), within project references UIDB/04106/2020 and UIDP/04106/2020. The second author was also supported by the FCT Sabbatical grant ref. SFRH/BSAB/143104/2018. The first author thanks the Foster G. and Mary McGaw Professorship in Mathematical Sciences, which supported this research. The second author wishes to thank also the support of the Portuguese Foundation for Science and Technology under the FCT Sabbatical grant. Publisher Copyright: {\textcopyright} 2021 Informa UK Limited, trading as Taylor & Francis Group.",
year = "2022",
month = jan,
day = "1",
doi = "10.1080/17442508.2021.2016766",
language = "English",
volume = "94",
pages = "926--958",
journal = "Stochastics",
issn = "1744-2508",
publisher = "Gordon and Breach Science Publishers",
number = "6",
}