Central limit theorem for a class of globally correlated random variables

Autores
Budini, Adrian Adolfo
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and statistics of the single variables, the corresponding sums are characterized by distinct probability densities. For a class of urn models it is also possible to characterize their domain of attraction, which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric q-Gaussian attractors (q<1) arise in a particular two-state case of these urn models.
Fil: Budini, Adrian Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Probability Theory, Stochastic Processes
Fluctuation Phenomena, Random Processes, Noise, And Brownian Motion
Systems Obeying Scaling Laws
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/61870
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/61870
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network_name_str CONICET Digital (CONICET)
spelling Central limit theorem for a class of globally correlated random variablesBudini, Adrian AdolfoProbability Theory, Stochastic ProcessesFluctuation Phenomena, Random Processes, Noise, And Brownian MotionSystems Obeying Scaling Lawshttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and statistics of the single variables, the corresponding sums are characterized by distinct probability densities. For a class of urn models it is also possible to characterize their domain of attraction, which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric q-Gaussian attractors (q<1) arise in a particular two-state case of these urn models.Fil: Budini, Adrian Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmerican Physical Society2016-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/61870Budini, Adrian Adolfo; Central limit theorem for a class of globally correlated random variables; American Physical Society; Physical Review E; 93; 6; 6-2016; 62114-621142470-0053CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.93.062114info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.062114info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T15:26:28Zoai:ri.conicet.gov.ar:11336/61870instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 15:26:28.399CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Central limit theorem for a class of globally correlated random variables
title Central limit theorem for a class of globally correlated random variables
spellingShingle Central limit theorem for a class of globally correlated random variables
Budini, Adrian Adolfo
Probability Theory, Stochastic Processes
Fluctuation Phenomena, Random Processes, Noise, And Brownian Motion
Systems Obeying Scaling Laws
title_short Central limit theorem for a class of globally correlated random variables
title_full Central limit theorem for a class of globally correlated random variables
title_fullStr Central limit theorem for a class of globally correlated random variables
title_full_unstemmed Central limit theorem for a class of globally correlated random variables
title_sort Central limit theorem for a class of globally correlated random variables
dc.creator.none.fl_str_mv Budini, Adrian Adolfo
author Budini, Adrian Adolfo
author_facet Budini, Adrian Adolfo
author_role author
dc.subject.none.fl_str_mv Probability Theory, Stochastic Processes
Fluctuation Phenomena, Random Processes, Noise, And Brownian Motion
Systems Obeying Scaling Laws
topic Probability Theory, Stochastic Processes
Fluctuation Phenomena, Random Processes, Noise, And Brownian Motion
Systems Obeying Scaling Laws
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and statistics of the single variables, the corresponding sums are characterized by distinct probability densities. For a class of urn models it is also possible to characterize their domain of attraction, which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric q-Gaussian attractors (q<1) arise in a particular two-state case of these urn models.
Fil: Budini, Adrian Adolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and statistics of the single variables, the corresponding sums are characterized by distinct probability densities. For a class of urn models it is also possible to characterize their domain of attraction, which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric q-Gaussian attractors (q<1) arise in a particular two-state case of these urn models.
publishDate 2016
dc.date.none.fl_str_mv 2016-06
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/61870
Budini, Adrian Adolfo; Central limit theorem for a class of globally correlated random variables; American Physical Society; Physical Review E; 93; 6; 6-2016; 62114-62114
2470-0053
CONICET Digital
CONICET
url http://hdl.handle.net/11336/61870
identifier_str_mv Budini, Adrian Adolfo; Central limit theorem for a class of globally correlated random variables; American Physical Society; Physical Review E; 93; 6; 6-2016; 62114-62114
2470-0053
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.93.062114
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.062114
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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