Probabilistic Stirling numbers and applications

We introduce probabilistic Stirling numbers of the first kind sY (n, k) associated with a complex-valued random variable Y satisfying appropriate integrability conditions, thus completing the notion of probabilistic Stirling numbers of the second kind SY (n, k) previously considered by the first aut...

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Detalhes bibliográficos
Autores: Adell, José A., Bényi, Beáta
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Recursos:Universidad de Zaragoza
Repositorio:Zaguán. Repositorio Digital de la Universidad de Zaragoza
OAI Identifier:oai:zaguan.unizar.es:135509
Acesso em linha:http://zaguan.unizar.es/record/135509
Access Level:acceso abierto
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spelling Probabilistic Stirling numbers and applicationsAdell, José A.Bényi, BeátaWe introduce probabilistic Stirling numbers of the first kind sY (n, k) associated with a complex-valued random variable Y satisfying appropriate integrability conditions, thus completing the notion of probabilistic Stirling numbers of the second kind SY (n, k) previously considered by the first author. Combinatorial interpretations, recursion formulas, and connections between sY (n, k) and SY (n, k) are given. We show that such numbers describe a large subset of potential polynomials, on the one hand, and the moments of sums of i. i. d. random variables, on the other, establishing their precise asymptotic behavior without appealing to the central limit theorem. We explicitly compute these numbers when Y has a certain familiar distribution, providing at the same time their combinatorial meaning.2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://zaguan.unizar.es/record/135509reponame:Zaguán. Repositorio Digital de la Universidad de Zaragozainstname:Universidad de ZaragozaInglésinfo:eu-repo/grantAgreement/ES/DGA/E48-23Rinfo:eu-repo/semantics/openAccessoai:zaguan.unizar.es:1355092026-05-29T13:59:51Z
dc.title.none.fl_str_mv Probabilistic Stirling numbers and applications
title Probabilistic Stirling numbers and applications
spellingShingle Probabilistic Stirling numbers and applications
Adell, José A.
title_short Probabilistic Stirling numbers and applications
title_full Probabilistic Stirling numbers and applications
title_fullStr Probabilistic Stirling numbers and applications
title_full_unstemmed Probabilistic Stirling numbers and applications
title_sort Probabilistic Stirling numbers and applications
dc.creator.none.fl_str_mv Adell, José A.
Bényi, Beáta
author Adell, José A.
author_facet Adell, José A.
Bényi, Beáta
author_role author
author2 Bényi, Beáta
author2_role author
description We introduce probabilistic Stirling numbers of the first kind sY (n, k) associated with a complex-valued random variable Y satisfying appropriate integrability conditions, thus completing the notion of probabilistic Stirling numbers of the second kind SY (n, k) previously considered by the first author. Combinatorial interpretations, recursion formulas, and connections between sY (n, k) and SY (n, k) are given. We show that such numbers describe a large subset of potential polynomials, on the one hand, and the moments of sums of i. i. d. random variables, on the other, establishing their precise asymptotic behavior without appealing to the central limit theorem. We explicitly compute these numbers when Y has a certain familiar distribution, providing at the same time their combinatorial meaning.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://zaguan.unizar.es/record/135509
url http://zaguan.unizar.es/record/135509
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/ES/DGA/E48-23R
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv
publisher.none.fl_str_mv
dc.source.none.fl_str_mv reponame:Zaguán. Repositorio Digital de la Universidad de Zaragoza
instname:Universidad de Zaragoza
instname_str Universidad de Zaragoza
reponame_str Zaguán. Repositorio Digital de la Universidad de Zaragoza
collection Zaguán. Repositorio Digital de la Universidad de Zaragoza
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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