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Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties

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Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties

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dc.contributor.author Calatayud-Gregori, Julia es_ES
dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Jornet-Sanz, Marc es_ES
dc.contributor.author Villafuerte, Laura es_ES
dc.date.accessioned 2019-05-16T20:01:13Z
dc.date.available 2019-05-16T20:01:13Z
dc.date.issued 2018 es_ES
dc.identifier.issn 1687-1847 es_ES
dc.identifier.uri http://hdl.handle.net/10251/120594
dc.description.abstract [EN] In this paper we study random non-autonomous second order linear differential equations by taking advantage of the powerful theory of random difference equations. The coefficients are assumed to be stochastic processes, and the initial conditions are random variables both defined in a common underlying complete probability space. Under appropriate assumptions established on the data stochastic processes and on the random initial conditions, and using key results on difference equations, we prove the existence of an analytic stochastic process solution in the random mean square sense. Truncating the random series that defines the solution process, we are able to approximate the main statistical properties of the solution, such as the expectation and the variance. We also obtain error a priori bounds to construct reliable approximations of both statistical moments. We include a set of numerical examples to illustrate the main theoretical results established throughout the paper. We finish with an example where our findings are combined with Monte Carlo simulations to model uncertainty using real data. es_ES
dc.description.sponsorship 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. es_ES
dc.language Inglés es_ES
dc.relation.ispartof Advances in Difference Equations es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Random second order linear difference and differential equation es_ES
dc.subject Analytic second order stochastic process es_ES
dc.subject L-p(Omega) es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1186/s13662-018-1848-8 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-89664-P/ES/PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Calatayud-Gregori, J.; Cortés, J.; Jornet-Sanz, M.; Villafuerte, L. (2018). Random non-autonomous second order linear differential equations: mean square analytic solutions and their statistical properties. Advances in Difference Equations. (3):1-29. https://doi.org/10.1186/s13662-018-1848-8 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://doi.org/10.1186/s13662-018-1848-8 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 29 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.issue 3 es_ES
dc.relation.pasarela S\370201 es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder Universitat Politècnica de València
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