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Improving Kernel Methods for Density Estimation in Random Differential Equations Problems

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Improving Kernel Methods for Density Estimation in Random Differential Equations Problems

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dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author Jornet Sanz, Marc es_ES
dc.date.accessioned 2021-02-20T04:31:26Z
dc.date.available 2021-02-20T04:31:26Z
dc.date.issued 2020-06 es_ES
dc.identifier.uri http://hdl.handle.net/10251/161986
dc.description.abstract [EN] Kernel density estimation is a non-parametric method to estimate the probability density function of a random quantity from a finite data sample. The estimator consists of a kernel function and a smoothing parameter called the bandwidth. Despite its undeniable usefulness, the convergence rate may be slow with the number of realizations and the discontinuity and peaked points of the target density may not be correctly captured. In this work, we analyze the applicability of a parametric method based on Monte Carlo simulation for the density estimation of certain random variable transformations. This approach has important applications in the setting of differential equations with input random parameters. es_ES
dc.description.sponsorship This work has been supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017-89664-P. es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematical and Computational Applications (Online) es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Probability density estimation es_ES
dc.subject Monte Carlo simulation es_ES
dc.subject Parametric method es_ES
dc.subject Random differential equation es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Improving Kernel Methods for Density Estimation in Random Differential Equations Problems es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/mca25020033 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 Cortés, J.; Jornet Sanz, M. (2020). Improving Kernel Methods for Density Estimation in Random Differential Equations Problems. Mathematical and Computational Applications (Online). 25(2):1-9. https://doi.org/10.3390/mca25020033 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/mca25020033 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 9 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 25 es_ES
dc.description.issue 2 es_ES
dc.identifier.eissn 2297-8747 es_ES
dc.relation.pasarela S\414102 es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES
dc.description.references Calatayud, J., Cortés, J.-C., Díaz, J. A., & Jornet, M. (2020). Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme. Applied Numerical Mathematics, 151, 413-424. doi:10.1016/j.apnum.2020.01.012 es_ES
dc.description.references Calatayud, J., Cortés, J.-C., & Jornet, M. (2018). The damped pendulum random differential equation: A comprehensive stochastic analysis via the computation of the probability density function. Physica A: Statistical Mechanics and its Applications, 512, 261-279. doi:10.1016/j.physa.2018.08.024 es_ES
dc.description.references Calatayud, J., Cortés, J.-C., Díaz, J. A., & Jornet, M. (2019). Density function of random differential equations via finite difference schemes: a theoretical analysis of a random diffusion-reaction Poisson-type problem. Stochastics, 92(4), 627-641. doi:10.1080/17442508.2019.1645849 es_ES
dc.description.references Calatayud, J., Cortés, J.-C., Dorini, F. A., & Jornet, M. (2020). Extending the study on the linear advection equation subject to stochastic velocity field and initial condition. Mathematics and Computers in Simulation, 172, 159-174. doi:10.1016/j.matcom.2019.12.014 es_ES
dc.description.references Jornet, M., Calatayud, J., Le Maître, O. P., & Cortés, J.-C. (2020). Second order linear differential equations with analytic uncertainties: Stochastic analysis via the computation of the probability density function. Journal of Computational and Applied Mathematics, 374, 112770. doi:10.1016/j.cam.2020.112770 es_ES
dc.description.references Tang, K., Wan, X., & Liao, Q. (2020). Deep density estimation via invertible block-triangular mapping. Theoretical and Applied Mechanics Letters, 10(3), 143-148. doi:10.1016/j.taml.2020.01.023 es_ES
dc.description.references Botev, Z., & Ridder, A. (2017). Variance Reduction. Wiley StatsRef: Statistics Reference Online, 1-6. doi:10.1002/9781118445112.stat07975 es_ES


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