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Probabilistic analysis of a class of impulsive linear random differential equations forced by stochastic processes admitting Karhunen-Loève expansions

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Probabilistic analysis of a class of impulsive linear random differential equations forced by stochastic processes admitting Karhunen-Loève expansions

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dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Delgadillo-Alemán, Sandra E. es_ES
dc.contributor.author Ku-Carrillo, Roberto A. es_ES
dc.contributor.author Villanueva Micó, Rafael Jacinto es_ES
dc.date.accessioned 2023-03-01T19:02:19Z
dc.date.available 2023-03-01T19:02:19Z
dc.date.issued 2022-09 es_ES
dc.identifier.issn 1937-1632 es_ES
dc.identifier.uri http://hdl.handle.net/10251/192215
dc.description.abstract [EN] We study a full randomization of the complete linear differential equation subject to an infinite train of Dirac's delta functions applied at different time instants. The initial condition and coefficients of the differential equation are assumed to be absolutely continuous random variables, while the external or forcing term is a stochastic process. We first approximate the forcing term using the Karhunen-Loeve expansion, and then we take advantage of the Random Variable Transformation method to construct a formal approximation of the first probability density function (1-p.d.f.) of the solution. By imposing mild conditions on the model parameters, we prove the convergence of the aforementioned approximation to the exact 1-p.d.f. of the solution. All the theoretical findings are illustrated by means of two examples, where different types of probability distributions are assumed to model parameters. es_ES
dc.description.sponsorship This work has been supported by the Spanish grants PID2020-115270GB-I00 funded by MCIN/AEI/10.13039/501100011033 and AICO/2021/302 (Generalitat Valenciana) , and also by the Mexican Council of Science and Technology (CONACYT) program "Apoyos complementarios para estancias sabaticas vinculadas a la consolidacion de grupo de investigacion" and the Universidad Autonoma de Aguascalientes, PIM21-5, PIM21-7. es_ES
dc.language Inglés es_ES
dc.publisher American Institute of Mathematical Sciences es_ES
dc.relation.ispartof Discrete and Continuous Dynamical Systems. Series S es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Random differential equation es_ES
dc.subject Dirac's delta impulses es_ES
dc.subject Karhunen-Loeve expansion es_ES
dc.subject Wiener process es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Probabilistic analysis of a class of impulsive linear random differential equations forced by stochastic processes admitting Karhunen-Loève expansions es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3934/dcdss.2022079 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-115270GB-I00/ES/ECUACIONES DIFERENCIALES ALEATORIAS. CUANTIFICACION DE LA INCERTIDUMBRE Y APLICACIONES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//AICO%2F2021%2F302/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UAA//PIM21-7/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/UAA//PIM21-5/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Facultad de Administración y Dirección de Empresas - Facultat d'Administració i Direcció d'Empreses es_ES
dc.description.bibliographicCitation Cortés, J.; Delgadillo-Alemán, SE.; Ku-Carrillo, RA.; Villanueva Micó, RJ. (2022). Probabilistic analysis of a class of impulsive linear random differential equations forced by stochastic processes admitting Karhunen-Loève expansions. Discrete and Continuous Dynamical Systems. Series S. 15(11):3131-3153. https://doi.org/10.3934/dcdss.2022079 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3934/dcdss.2022079 es_ES
dc.description.upvformatpinicio 3131 es_ES
dc.description.upvformatpfin 3153 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 15 es_ES
dc.description.issue 11 es_ES
dc.relation.pasarela S\456052 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder AGENCIA ESTATAL DE INVESTIGACION es_ES
dc.contributor.funder Universidad Autónoma de Aguascalientes es_ES
dc.contributor.funder Consejo Nacional de Ciencia y Tecnología, México es_ES
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