Solving random homogeneous linear second-order differential equations: a full probabilistic description

[EN] In this paper a complete probabilistic description for the solution of random homogeneous linear second-order differential equations via the computation of its two first probability density functions is given. As a consequence, all unidimensional and two-dimensional statistical moments can be s...

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Detalhes bibliográficos
Autores: M.-C. Casabán|||0000-0002-5708-5709, Cortés, J.-C.|||0000-0002-6528-2155, Romero, José-Vicente|||0000-0003-3366-6557, Roselló, María-Dolores|||0000-0002-5724-7683
Formato: artículo
Fecha de publicación:2016
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:10251/94531
Acesso em linha:https://riunet.upv.es/handle/10251/94531
Access Level:acceso abierto
Palavra-chave:Random variable transformation method
First and second probability density functions
Random homogeneous linear second-order differential equations.
MATEMATICA APLICADA
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spelling Solving random homogeneous linear second-order differential equations: a full probabilistic descriptionM.-C. Casabán|||0000-0002-5708-5709Cortés, J.-C.|||0000-0002-6528-2155Romero, José-Vicente|||0000-0003-3366-6557Roselló, María-Dolores|||0000-0002-5724-7683Random variable transformation methodFirst and second probability density functionsRandom homogeneous linear second-order differential equations.MATEMATICA APLICADA[EN] In this paper a complete probabilistic description for the solution of random homogeneous linear second-order differential equations via the computation of its two first probability density functions is given. As a consequence, all unidimensional and two-dimensional statistical moments can be straightforwardly determined, in particular, mean, variance and covariance functions, as well as the first-order conditional law. With the aim of providing more generality, in a first step, all involved input parameters are assumed to be statistically dependent random variables having an arbitrary joint probability density function. Second, the particular case that just initial conditions are random variables is also analysed. Both problems have common and distinctive feature which are highlighted in our analysis. The study is based on random variable transformation method. As a consequence of our study, the well-known deterministic results are nicely generalized. Several illustrative examples are included.This work has been partially supported by the Spanish M. C. Y. T. Grant MTM2013-41765-P.Springer-VerlagEscuela Técnica Superior de Ingeniería de TelecomunicaciónFacultad de Administración y Dirección de EmpresasDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialInstituto Universitario de Matemática MultidisciplinarEscuela Técnica Superior de Ingeniería Agronómica y del Medio NaturalMinisterio de Economía, Industria y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20162016-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/94531reponame: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:10251/945312026-06-13T07:49:27Z
dc.title.none.fl_str_mv Solving random homogeneous linear second-order differential equations: a full probabilistic description
title Solving random homogeneous linear second-order differential equations: a full probabilistic description
spellingShingle Solving random homogeneous linear second-order differential equations: a full probabilistic description
M.-C. Casabán|||0000-0002-5708-5709
Random variable transformation method
First and second probability density functions
Random homogeneous linear second-order differential equations.
MATEMATICA APLICADA
title_short Solving random homogeneous linear second-order differential equations: a full probabilistic description
title_full Solving random homogeneous linear second-order differential equations: a full probabilistic description
title_fullStr Solving random homogeneous linear second-order differential equations: a full probabilistic description
title_full_unstemmed Solving random homogeneous linear second-order differential equations: a full probabilistic description
title_sort Solving random homogeneous linear second-order differential equations: a full probabilistic description
dc.creator.none.fl_str_mv M.-C. Casabán|||0000-0002-5708-5709
Cortés, J.-C.|||0000-0002-6528-2155
Romero, José-Vicente|||0000-0003-3366-6557
Roselló, María-Dolores|||0000-0002-5724-7683
author M.-C. Casabán|||0000-0002-5708-5709
author_facet M.-C. Casabán|||0000-0002-5708-5709
Cortés, J.-C.|||0000-0002-6528-2155
Romero, José-Vicente|||0000-0003-3366-6557
Roselló, María-Dolores|||0000-0002-5724-7683
author_role author
author2 Cortés, J.-C.|||0000-0002-6528-2155
Romero, José-Vicente|||0000-0003-3366-6557
Roselló, María-Dolores|||0000-0002-5724-7683
author2_role author
author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Facultad de Administración y Dirección de Empresas
Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Instituto Universitario de Matemática Multidisciplinar
Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural
Ministerio de Economía, Industria y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Random variable transformation method
First and second probability density functions
Random homogeneous linear second-order differential equations.
MATEMATICA APLICADA
topic Random variable transformation method
First and second probability density functions
Random homogeneous linear second-order differential equations.
MATEMATICA APLICADA
description [EN] In this paper a complete probabilistic description for the solution of random homogeneous linear second-order differential equations via the computation of its two first probability density functions is given. As a consequence, all unidimensional and two-dimensional statistical moments can be straightforwardly determined, in particular, mean, variance and covariance functions, as well as the first-order conditional law. With the aim of providing more generality, in a first step, all involved input parameters are assumed to be statistically dependent random variables having an arbitrary joint probability density function. Second, the particular case that just initial conditions are random variables is also analysed. Both problems have common and distinctive feature which are highlighted in our analysis. The study is based on random variable transformation method. As a consequence of our study, the well-known deterministic results are nicely generalized. Several illustrative examples are included.
publishDate 2016
dc.date.none.fl_str_mv 2016
2016-01-01
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/10251/94531
url https://riunet.upv.es/handle/10251/94531
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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