A mean square chain rule and its application in solving the random Chebyshev differential equation

[EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assum...

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Detalhes bibliográficos
Autores: Cortés, J.-C.|||0000-0002-6528-2155, Burgos-Simon, Clara|||0000-0001-6385-4263, Villafuerte, Laura
Formato: artículo
Fecha de publicación:2017
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/105851
Acesso em linha:https://riunet.upv.es/handle/10251/105851
Access Level:acceso abierto
Palavra-chave:Mean square chain rule
Random Chebyshev differential equation
Mean square and mean fourth calculus
Monte Carlo simulations
MATEMATICA APLICADA
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spelling A mean square chain rule and its application in solving the random Chebyshev differential equationCortés, J.-C.|||0000-0002-6528-2155Burgos-Simon, Clara|||0000-0001-6385-4263Villafuerte, LauraMean square chain ruleRandom Chebyshev differential equationMean square and mean fourth calculusMonte Carlo simulationsMATEMATICA APLICADA[EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assuming mild moment hypotheses on the random variables that appear as coefficients and initial conditions of the cor- responding initial value problem. Such solution is represented through a mean square random power series. Moreover, reliable approximations for the mean and standard deviation functions to the solution stochastic process of the r.C.d.e. are given. Several examples, that illustrate the theoretical results, are included.This work was completed with the support of our TEX-pert.Springer-VerlagFacultad de Administración y Dirección de EmpresasDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Geodésica, Cartográfica y TopográficaInstituto Universitario de Matemática MultidisciplinarMinisterio de Economía, Industria y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20172017-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/105851reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengMinisterio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2013-41765-P METODOS COMPUTACIONALES PARA ECUACIONES DIFERENCIALES ALEATORIAS: TEORIA Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1058512026-06-13T07:49:27Z
dc.title.none.fl_str_mv A mean square chain rule and its application in solving the random Chebyshev differential equation
title A mean square chain rule and its application in solving the random Chebyshev differential equation
spellingShingle A mean square chain rule and its application in solving the random Chebyshev differential equation
Cortés, J.-C.|||0000-0002-6528-2155
Mean square chain rule
Random Chebyshev differential equation
Mean square and mean fourth calculus
Monte Carlo simulations
MATEMATICA APLICADA
title_short A mean square chain rule and its application in solving the random Chebyshev differential equation
title_full A mean square chain rule and its application in solving the random Chebyshev differential equation
title_fullStr A mean square chain rule and its application in solving the random Chebyshev differential equation
title_full_unstemmed A mean square chain rule and its application in solving the random Chebyshev differential equation
title_sort A mean square chain rule and its application in solving the random Chebyshev differential equation
dc.creator.none.fl_str_mv Cortés, J.-C.|||0000-0002-6528-2155
Burgos-Simon, Clara|||0000-0001-6385-4263
Villafuerte, Laura
author Cortés, J.-C.|||0000-0002-6528-2155
author_facet Cortés, J.-C.|||0000-0002-6528-2155
Burgos-Simon, Clara|||0000-0001-6385-4263
Villafuerte, Laura
author_role author
author2 Burgos-Simon, Clara|||0000-0001-6385-4263
Villafuerte, Laura
author2_role author
author
dc.contributor.none.fl_str_mv Facultad de Administración y Dirección de Empresas
Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Geodésica, Cartográfica y Topográfica
Instituto Universitario de Matemática Multidisciplinar
Ministerio de Economía, Industria y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Mean square chain rule
Random Chebyshev differential equation
Mean square and mean fourth calculus
Monte Carlo simulations
MATEMATICA APLICADA
topic Mean square chain rule
Random Chebyshev differential equation
Mean square and mean fourth calculus
Monte Carlo simulations
MATEMATICA APLICADA
description [EN] In this paper a new version of the chain rule for calculat- ing the mean square derivative of a second-order stochastic process is proven. This random operational calculus rule is applied to construct a rigorous mean square solution of the random Chebyshev differential equation (r.C.d.e.) assuming mild moment hypotheses on the random variables that appear as coefficients and initial conditions of the cor- responding initial value problem. Such solution is represented through a mean square random power series. Moreover, reliable approximations for the mean and standard deviation functions to the solution stochastic process of the r.C.d.e. are given. Several examples, that illustrate the theoretical results, are included.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/105851
url https://riunet.upv.es/handle/10251/105851
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2013-41765-P METODOS COMPUTACIONALES PARA ECUACIONES DIFERENCIALES ALEATORIAS: TEORIA Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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