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Symmetry 2019, 11(1), 43; https://doi.org/10.3390/sym11010043

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

1
Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 Valencia, Spain
2
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA
*
Author to whom correspondence should be addressed.
Received: 15 November 2018 / Revised: 28 December 2018 / Accepted: 30 December 2018 / Published: 3 January 2019
(This article belongs to the Special Issue Mathematical Epidemiology in Medicine & Social Sciences)
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Abstract

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. View Full-Text
Keywords: uncertainty quantification; epidemiological stochastic model; probability density function; generalized polynomial chaos; random variable transformation technique uncertainty quantification; epidemiological stochastic model; probability density function; generalized polynomial chaos; random variable transformation technique
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Calatayud Gregori, J.; Chen-Charpentier, B.M.; Cortés López, J.C.; Jornet Sanz, M. Combining Polynomial Chaos Expansions and the Random Variable Transformation Technique to Approximate the Density Function of Stochastic Problems, Including Some Epidemiological Models. Symmetry 2019, 11, 43.

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