Generalized white noise analysis and topological algebras

Detalhes bibliográficos
Autor(a) principal: Alpay, Daniel
Data de Publicação: 2022
Outros Autores: Cerejeiras, Paula, Kahler, Uwe
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/35088
Resumo: 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.
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spelling Generalized white noise analysis and topological algebrasNon-Gaussian analysisGrey noise spaceGeneralized fock spaceStrong algebrasIn 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.Taylor & Francis2023-09-30T00:00:00Z2022-01-01T00:00:00Z2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/35088eng1744-250810.1080/17442508.2021.2016766Alpay, DanielCerejeiras, PaulaKahler, Uweinfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T12:07:08Zoai:ria.ua.pt:10773/35088Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:06:00.061795Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Generalized white noise analysis and topological algebras
title Generalized white noise analysis and topological algebras
spellingShingle Generalized white noise analysis and topological algebras
Alpay, Daniel
Non-Gaussian analysis
Grey noise space
Generalized fock space
Strong algebras
title_short Generalized white noise analysis and topological algebras
title_full Generalized white noise analysis and topological algebras
title_fullStr Generalized white noise analysis and topological algebras
title_full_unstemmed Generalized white noise analysis and topological algebras
title_sort Generalized white noise analysis and topological algebras
author Alpay, Daniel
author_facet Alpay, Daniel
Cerejeiras, Paula
Kahler, Uwe
author_role author
author2 Cerejeiras, Paula
Kahler, Uwe
author2_role author
author
dc.contributor.author.fl_str_mv Alpay, Daniel
Cerejeiras, Paula
Kahler, Uwe
dc.subject.por.fl_str_mv Non-Gaussian analysis
Grey noise space
Generalized fock space
Strong algebras
topic Non-Gaussian analysis
Grey noise space
Generalized fock space
Strong algebras
description 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.
publishDate 2022
dc.date.none.fl_str_mv 2022-01-01T00:00:00Z
2022
2023-09-30T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10773/35088
url http://hdl.handle.net/10773/35088
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1744-2508
10.1080/17442508.2021.2016766
dc.rights.driver.fl_str_mv info:eu-repo/semantics/embargoedAccess
eu_rights_str_mv embargoedAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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