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Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models

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Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models

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dc.contributor.author Calatayud-Gregori, Julia es_ES
dc.contributor.author Chen-Charpentier, Benito M. es_ES
dc.contributor.author Cortés, J.C. es_ES
dc.contributor.author Jornet-Sanz, Marc es_ES
dc.date.accessioned 2020-04-07T05:49:41Z
dc.date.available 2020-04-07T05:49:41Z
dc.date.issued 2019-01 es_ES
dc.identifier.uri http://hdl.handle.net/10251/140420
dc.description.abstract [EN] In this paper, we deal with computational uncertainty quantification for stochastic models with one random input parameter. The goal of the paper is twofold: First, to approximate the set of probability density functions of the solution stochastic process, and second, to show the capability of our theoretical findings to deal with some important epidemiological models. The approximations are constructed in terms of a polynomial evaluated at the random input parameter, by means of generalized polynomial chaos expansions and the stochastic Galerkin projection technique. The probability density function of the aforementioned univariate polynomial is computed via the random variable transformation method, by taking into account the domains where the polynomial is strictly monotone. The algebraic/exponential convergence of the Galerkin projections gives rapid convergence of these density functions. The examples are based on fundamental epidemiological models formulated via linear and nonlinear differential and difference equations, where one of the input parameters is assumed to be a random variable. es_ES
dc.description.sponsorship This work has been supported by the Spanish Ministerio de Economia y Competitividad grant MTM2017-89664-P. The author 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.publisher MDPI AG es_ES
dc.relation.ispartof Symmetry (Basel) es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Uncertainty quantification es_ES
dc.subject Epidemiological stochastic model es_ES
dc.subject Probability density function es_ES
dc.subject Generalized polynomial chaos es_ES
dc.subject Random variable transformation technique es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/sym11010043 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.; Chen-Charpentier, BM.; Cortés, J.; Jornet-Sanz, M. (2019). Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models. Symmetry (Basel). 11(1):1-28. https://doi.org/10.3390/sym11010043 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/sym11010043 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 28 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 11 es_ES
dc.description.issue 1 es_ES
dc.identifier.eissn 2073-8994 es_ES
dc.relation.pasarela S\374690 es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder Universitat Politècnica de València es_ES
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