Discretisations of higher order and the theorems of

Detalhes bibliográficos
Autor(a) principal: Van den Berg, Imme
Data de Publicação: 2013
Tipo de documento: Artigo
Idioma: por
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10174/9637
Resumo: We study discrete functions on equidistant and nonequidistant infinitesimal grids. We consider their difference quotients of higher order and give conditions for their nearequality to the corresponding derivatives. Important tools are nonstandard notions of regularity of higher order, and the formula of Fa`a di Bruno for higher order derivatives and a iscrete version of it. As an application of such transitions from the discrete to the continuous we extend the DeMoivreLaplace Theorem to higher order: nth order difference quotients of the binomial probability distribution tend to the corresponding nth order partial differential quotients of the Gaussian distribution.
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spelling Discretisations of higher order and the theorems ofDifference quotientsChain ruleFa`a di Bruno TheoremDeMoivreLaplacenonstandard analysisWe study discrete functions on equidistant and nonequidistant infinitesimal grids. We consider their difference quotients of higher order and give conditions for their nearequality to the corresponding derivatives. Important tools are nonstandard notions of regularity of higher order, and the formula of Fa`a di Bruno for higher order derivatives and a iscrete version of it. As an application of such transitions from the discrete to the continuous we extend the DeMoivreLaplace Theorem to higher order: nth order difference quotients of the binomial probability distribution tend to the corresponding nth order partial differential quotients of the Gaussian distribution.Association of Symbolic Logic2014-01-15T11:43:31Z2014-01-152013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10174/9637http://hdl.handle.net/10174/9637porImme van den Berg, Discretisations of higher order and the theorems of Fa`a di Bruno and DeMoivreLaplace, Journal of Logic & Analysis 5:6 (2013) 1–35 ISSN 175990081759-9008http://logicandanalysis.org/index.php/jla/article/viewFile/173/87ivdb@uevora.pt334Van den Berg, Immeinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-01-03T18:51:41Zoai:dspace.uevora.pt:10174/9637Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T01:03:39.437232Repositório 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 Discretisations of higher order and the theorems of
title Discretisations of higher order and the theorems of
spellingShingle Discretisations of higher order and the theorems of
Van den Berg, Imme
Difference quotients
Chain rule
Fa`a di Bruno Theorem
DeMoivreLaplace
nonstandard analysis
title_short Discretisations of higher order and the theorems of
title_full Discretisations of higher order and the theorems of
title_fullStr Discretisations of higher order and the theorems of
title_full_unstemmed Discretisations of higher order and the theorems of
title_sort Discretisations of higher order and the theorems of
author Van den Berg, Imme
author_facet Van den Berg, Imme
author_role author
dc.contributor.author.fl_str_mv Van den Berg, Imme
dc.subject.por.fl_str_mv Difference quotients
Chain rule
Fa`a di Bruno Theorem
DeMoivreLaplace
nonstandard analysis
topic Difference quotients
Chain rule
Fa`a di Bruno Theorem
DeMoivreLaplace
nonstandard analysis
description We study discrete functions on equidistant and nonequidistant infinitesimal grids. We consider their difference quotients of higher order and give conditions for their nearequality to the corresponding derivatives. Important tools are nonstandard notions of regularity of higher order, and the formula of Fa`a di Bruno for higher order derivatives and a iscrete version of it. As an application of such transitions from the discrete to the continuous we extend the DeMoivreLaplace Theorem to higher order: nth order difference quotients of the binomial probability distribution tend to the corresponding nth order partial differential quotients of the Gaussian distribution.
publishDate 2013
dc.date.none.fl_str_mv 2013-01-01T00:00:00Z
2014-01-15T11:43:31Z
2014-01-15
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/10174/9637
http://hdl.handle.net/10174/9637
url http://hdl.handle.net/10174/9637
dc.language.iso.fl_str_mv por
language por
dc.relation.none.fl_str_mv Imme van den Berg, Discretisations of higher order and the theorems of Fa`a di Bruno and DeMoivreLaplace, Journal of Logic & Analysis 5:6 (2013) 1–35 ISSN 17599008
1759-9008
http://logicandanalysis.org/index.php/jla/article/viewFile/173/87
ivdb@uevora.pt
334
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Association of Symbolic Logic
publisher.none.fl_str_mv Association of Symbolic Logic
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
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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
repository.mail.fl_str_mv
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