Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem

[EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this computational method has not been performed in the extant literature. In this...

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Autores: Calatayud, J., Díaz, J.A., Jornet, M., Cortés, J.-C.|||0000-0002-6528-2155
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/161848
Acceso en línea:https://riunet.upv.es/handle/10251/161848
Access Level:acceso abierto
Palabra clave:Random diffusion-reaction Poisson-type problem
Finite difference scheme
Probability density function
Numerical methods
MATEMATICA APLICADA
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spelling Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problemCalatayud, J.Díaz, J.A.Jornet, M.Cortés, J.-C.|||0000-0002-6528-2155Random diffusion-reaction Poisson-type problemFinite difference schemeProbability density functionNumerical methodsMATEMATICA APLICADA[EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this computational method has not been performed in the extant literature. In this paper, we deal with a particular random differential equation: a random diffusion-reaction Poisson-type problem of the form , , with boundary conditions , . Here, alpha, A and B are random variables and is a stochastic process. The term is a stochastic process that solves the random problem in the sample path sense. Via a finite difference scheme, we approximate with a sequence of stochastic processes in both the almost sure and senses. This allows us to find mild conditions under which the probability density function of can be approximated. Illustrative examples are included.This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. Marc Jornet acknowledges the doctorate scholarship granted by Programa de Ayudas de Investigacion y Desarrollo (PAID), Universitat Politecnica de Valencia.Taylor & FrancisFacultad de Administración y Dirección de EmpresasDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarAgencia Estatal de InvestigaciónUniversitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-05-18journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/161848reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-89664-P PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION 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:10251/1618482026-06-13T07:49:27Z
dc.title.none.fl_str_mv Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
title Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
spellingShingle Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
Calatayud, J.
Random diffusion-reaction Poisson-type problem
Finite difference scheme
Probability density function
Numerical methods
MATEMATICA APLICADA
title_short Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
title_full Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
title_fullStr Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
title_full_unstemmed Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
title_sort Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem
dc.creator.none.fl_str_mv Calatayud, J.
Díaz, J.A.
Jornet, M.
Cortés, J.-C.|||0000-0002-6528-2155
author Calatayud, J.
author_facet Calatayud, J.
Díaz, J.A.
Jornet, M.
Cortés, J.-C.|||0000-0002-6528-2155
author_role author
author2 Díaz, J.A.
Jornet, M.
Cortés, J.-C.|||0000-0002-6528-2155
author2_role author
author
author
dc.contributor.none.fl_str_mv Facultad de Administración y Dirección de Empresas
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
Agencia Estatal de Investigación
Universitat Politècnica de València
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Random diffusion-reaction Poisson-type problem
Finite difference scheme
Probability density function
Numerical methods
MATEMATICA APLICADA
topic Random diffusion-reaction Poisson-type problem
Finite difference scheme
Probability density function
Numerical methods
MATEMATICA APLICADA
description [EN] A computational approach to approximate the probability density function of random differential equations is based on transformation of random variables and finite difference schemes. The theoretical analysis of this computational method has not been performed in the extant literature. In this paper, we deal with a particular random differential equation: a random diffusion-reaction Poisson-type problem of the form , , with boundary conditions , . Here, alpha, A and B are random variables and is a stochastic process. The term is a stochastic process that solves the random problem in the sample path sense. Via a finite difference scheme, we approximate with a sequence of stochastic processes in both the almost sure and senses. This allows us to find mild conditions under which the probability density function of can be approximated. Illustrative examples are included.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-05-18
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/10251/161848
url https://riunet.upv.es/handle/10251/161848
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-89664-P PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION 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 Taylor & Francis
publisher.none.fl_str_mv Taylor & Francis
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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