The Experts below are selected from a list of 41979 Experts worldwide ranked by ideXlab platform
M D Rosello - One of the best experts on this subject based on the ideXlab platform.
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improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2017Co-Authors: J C Cortes, J V Romero, M D Rosello, Rafaeljacinto VillanuevaAbstract:Abstract Generalized polynomial chaos (gPC) is a spectral technique in random space to represent random Variables and stochastic processes in terms of orthogonal polynomials of the Askey scheme. One of its most fruitful applications consists of solving random differential equations. With gPC, stochastic solutions are expressed as orthogonal polynomials of the input random parameters. Different types of orthogonal polynomials can be chosen to achieve better convergence. This choice is dictated by the key correspondence between the weight function associated to orthogonal polynomials in the Askey scheme and the probability density functions of standard random Variables. Otherwise, adaptive gPC constitutes a complementary spectral method to deal with arbitrary random Variables in random differential equations. In its original formulation, adaptive gPC requires that both the unknowns and input random parameters enter polynomially in random differential equations. Regarding the inputs, if they appear as non-polynomial mappings of themselves, polynomial approximations are required and, as a consequence, loss of accuracy will be carried out in computations. In this paper an extended version of adaptive gPC is developed to circumvent these limitations of adaptive gPC by taking advantage of the random Variable Transformation method. A number of illustrative examples show the superiority of the extended adaptive gPC for solving nonlinear random differential equations. In addition, for the sake of completeness, in all examples randomness is tackled by nonlinear expressions.
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a comprehensive probabilistic solution of random sis type epidemiological models using the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2016Co-Authors: M C Casaban, J C Cortes, A Navarroquiles, J V Romero, M D Rosello, R J VillanuevaAbstract:Abstract This paper provides a complete probabilistic description of SIS-type epidemiological models where all the input parameters (contagion rate, recovery rate and initial conditions) are assumed to be random Variables. By applying the Random Variable Transformation technique, the first probability density function, the mean and the variance functions, as well as confidence intervals associated with the solution of SIS-type epidemiological models, are determined. It is done under the general hypothesis that model random inputs have any joint probability density function. The distributions to describe the time until a given proportion of the population remains susceptible and infected are also determined. Finally, a probabilistic description of the so-called basic reproductive number is included. The theoretical results are applied to an illustrative example showing good fitting.
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probabilistic solution of random si type epidemiological models using the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: M C Casaban, J C Cortes, J V Romero, M D RoselloAbstract:Abstract This paper presents a full probabilistic description of the solution of random SI-type epidemiological models which are based on nonlinear differential equations. This description consists of determining: the first probability density function of the solution in terms of the density functions of the diffusion coefficient and the initial condition, which are assumed to be independent random Variables; the expectation and variance functions of the solution as well as confidence intervals and, finally, the distribution of time until a given proportion of susceptibles remains in the population. The obtained formulas are general since they are valid regardless the probability distributions assigned to the random inputs. We also present a pair of illustrative examples including in one of them the application of the theoretical results to model the diffusion of a technology using real data.
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determining the first probability density function of linear random initial value problems by the random Variable Transformation rvt technique a comprehensive study
Abstract and Applied Analysis, 2014Co-Authors: M C Casaban, J C Cortes, J V Romero, M D RoselloAbstract:Deterministic differential equations are useful tools for mathematical modelling. The consideration of uncertainty into their formulation leads to random differential equations. Solving a random differential equation means computing not only its solution stochastic process but also its main statistical functions such as the expectation and standard deviation. The determination of its first probability density function provides a more complete probabilistic description of the solution stochastic process in each time instant. In this paper, one presents a comprehensive study to determinate the first probability density function to the solution of linear random initial value problems taking advantage of the so-called random Variable Transformation method. For the sake of clarity, the study has been split into thirteen cases depending on the way that randomness enters into the linear model. In most cases, the analysis includes the specification of the domain of the first probability density function of the solution stochastic process whose determination is a delicate issue. A strong point of the study is the presentation of a wide range of examples, at least one of each of the thirteen casuistries, where both standard and nonstandard probabilistic distributions are considered.
J C Cortes - One of the best experts on this subject based on the ideXlab platform.
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applying the random Variable Transformation method to solve a class of random linear differential equation with discrete delay
Applied Mathematics and Computation, 2019Co-Authors: Tomas Caraballo, J C Cortes, A NavarroquilesAbstract:Abstract We randomize the following class of linear differential equations with delay, x τ ′ ( t ) = a x τ ( t ) + b x τ ( t − τ ) , t > 0, and initial condition, x τ ( t ) = g ( t ) , − τ ≤ t ≤ 0 , by assuming that coefficients a and b are random Variables and the initial condition g(t) is a stochastic process. We consider two cases, depending on the functional form of the stochastic process g(t), and then we solve, from a probabilistic point of view, both random initial value problems by determining explicit expressions to the first probability density function, f(x, t; τ), of the corresponding solution stochastic processes. Afterwards, we establish sufficient conditions on the involved random input parameters in order to guarantee that f(x, t; τ) converges, as τ → 0 + , to the first probability density function, say f(x, t), of the corresponding associated random linear problem without delay ( τ = 0 ). The paper concludes with several numerical experiments illustrating our theoretical findings.
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a full probabilistic solution of the random linear fractional differential equation via the random Variable Transformation technique
Mathematical Methods in The Applied Sciences, 2018Co-Authors: Clara Burgossimon, J C Cortes, Julia Calatayudgregori, A NavarroquilesAbstract:Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-P; Programa de Ayudas de Investigacion y Desarrollo, Grant/Award Number: PAID-2014; UNiversitat Politecncia de Valencia
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improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2017Co-Authors: J C Cortes, J V Romero, M D Rosello, Rafaeljacinto VillanuevaAbstract:Abstract Generalized polynomial chaos (gPC) is a spectral technique in random space to represent random Variables and stochastic processes in terms of orthogonal polynomials of the Askey scheme. One of its most fruitful applications consists of solving random differential equations. With gPC, stochastic solutions are expressed as orthogonal polynomials of the input random parameters. Different types of orthogonal polynomials can be chosen to achieve better convergence. This choice is dictated by the key correspondence between the weight function associated to orthogonal polynomials in the Askey scheme and the probability density functions of standard random Variables. Otherwise, adaptive gPC constitutes a complementary spectral method to deal with arbitrary random Variables in random differential equations. In its original formulation, adaptive gPC requires that both the unknowns and input random parameters enter polynomially in random differential equations. Regarding the inputs, if they appear as non-polynomial mappings of themselves, polynomial approximations are required and, as a consequence, loss of accuracy will be carried out in computations. In this paper an extended version of adaptive gPC is developed to circumvent these limitations of adaptive gPC by taking advantage of the random Variable Transformation method. A number of illustrative examples show the superiority of the extended adaptive gPC for solving nonlinear random differential equations. In addition, for the sake of completeness, in all examples randomness is tackled by nonlinear expressions.
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a comprehensive probabilistic solution of random sis type epidemiological models using the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2016Co-Authors: M C Casaban, J C Cortes, A Navarroquiles, J V Romero, M D Rosello, R J VillanuevaAbstract:Abstract This paper provides a complete probabilistic description of SIS-type epidemiological models where all the input parameters (contagion rate, recovery rate and initial conditions) are assumed to be random Variables. By applying the Random Variable Transformation technique, the first probability density function, the mean and the variance functions, as well as confidence intervals associated with the solution of SIS-type epidemiological models, are determined. It is done under the general hypothesis that model random inputs have any joint probability density function. The distributions to describe the time until a given proportion of the population remains susceptible and infected are also determined. Finally, a probabilistic description of the so-called basic reproductive number is included. The theoretical results are applied to an illustrative example showing good fitting.
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probabilistic solution of random si type epidemiological models using the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: M C Casaban, J C Cortes, J V Romero, M D RoselloAbstract:Abstract This paper presents a full probabilistic description of the solution of random SI-type epidemiological models which are based on nonlinear differential equations. This description consists of determining: the first probability density function of the solution in terms of the density functions of the diffusion coefficient and the initial condition, which are assumed to be independent random Variables; the expectation and variance functions of the solution as well as confidence intervals and, finally, the distribution of time until a given proportion of susceptibles remains in the population. The obtained formulas are general since they are valid regardless the probability distributions assigned to the random inputs. We also present a pair of illustrative examples including in one of them the application of the theoretical results to model the diffusion of a technology using real data.
M C Casaban - One of the best experts on this subject based on the ideXlab platform.
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a comprehensive probabilistic solution of random sis type epidemiological models using the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2016Co-Authors: M C Casaban, J C Cortes, A Navarroquiles, J V Romero, M D Rosello, R J VillanuevaAbstract:Abstract This paper provides a complete probabilistic description of SIS-type epidemiological models where all the input parameters (contagion rate, recovery rate and initial conditions) are assumed to be random Variables. By applying the Random Variable Transformation technique, the first probability density function, the mean and the variance functions, as well as confidence intervals associated with the solution of SIS-type epidemiological models, are determined. It is done under the general hypothesis that model random inputs have any joint probability density function. The distributions to describe the time until a given proportion of the population remains susceptible and infected are also determined. Finally, a probabilistic description of the so-called basic reproductive number is included. The theoretical results are applied to an illustrative example showing good fitting.
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probabilistic solution of random si type epidemiological models using the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: M C Casaban, J C Cortes, J V Romero, M D RoselloAbstract:Abstract This paper presents a full probabilistic description of the solution of random SI-type epidemiological models which are based on nonlinear differential equations. This description consists of determining: the first probability density function of the solution in terms of the density functions of the diffusion coefficient and the initial condition, which are assumed to be independent random Variables; the expectation and variance functions of the solution as well as confidence intervals and, finally, the distribution of time until a given proportion of susceptibles remains in the population. The obtained formulas are general since they are valid regardless the probability distributions assigned to the random inputs. We also present a pair of illustrative examples including in one of them the application of the theoretical results to model the diffusion of a technology using real data.
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determining the first probability density function of linear random initial value problems by the random Variable Transformation rvt technique a comprehensive study
Abstract and Applied Analysis, 2014Co-Authors: M C Casaban, J C Cortes, J V Romero, M D RoselloAbstract:Deterministic differential equations are useful tools for mathematical modelling. The consideration of uncertainty into their formulation leads to random differential equations. Solving a random differential equation means computing not only its solution stochastic process but also its main statistical functions such as the expectation and standard deviation. The determination of its first probability density function provides a more complete probabilistic description of the solution stochastic process in each time instant. In this paper, one presents a comprehensive study to determinate the first probability density function to the solution of linear random initial value problems taking advantage of the so-called random Variable Transformation method. For the sake of clarity, the study has been split into thirteen cases depending on the way that randomness enters into the linear model. In most cases, the analysis includes the specification of the domain of the first probability density function of the solution stochastic process whose determination is a delicate issue. A strong point of the study is the presentation of a wide range of examples, at least one of each of the thirteen casuistries, where both standard and nonstandard probabilistic distributions are considered.
J V Romero - One of the best experts on this subject based on the ideXlab platform.
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improving adaptive generalized polynomial chaos method to solve nonlinear random differential equations by the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2017Co-Authors: J C Cortes, J V Romero, M D Rosello, Rafaeljacinto VillanuevaAbstract:Abstract Generalized polynomial chaos (gPC) is a spectral technique in random space to represent random Variables and stochastic processes in terms of orthogonal polynomials of the Askey scheme. One of its most fruitful applications consists of solving random differential equations. With gPC, stochastic solutions are expressed as orthogonal polynomials of the input random parameters. Different types of orthogonal polynomials can be chosen to achieve better convergence. This choice is dictated by the key correspondence between the weight function associated to orthogonal polynomials in the Askey scheme and the probability density functions of standard random Variables. Otherwise, adaptive gPC constitutes a complementary spectral method to deal with arbitrary random Variables in random differential equations. In its original formulation, adaptive gPC requires that both the unknowns and input random parameters enter polynomially in random differential equations. Regarding the inputs, if they appear as non-polynomial mappings of themselves, polynomial approximations are required and, as a consequence, loss of accuracy will be carried out in computations. In this paper an extended version of adaptive gPC is developed to circumvent these limitations of adaptive gPC by taking advantage of the random Variable Transformation method. A number of illustrative examples show the superiority of the extended adaptive gPC for solving nonlinear random differential equations. In addition, for the sake of completeness, in all examples randomness is tackled by nonlinear expressions.
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a comprehensive probabilistic solution of random sis type epidemiological models using the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2016Co-Authors: M C Casaban, J C Cortes, A Navarroquiles, J V Romero, M D Rosello, R J VillanuevaAbstract:Abstract This paper provides a complete probabilistic description of SIS-type epidemiological models where all the input parameters (contagion rate, recovery rate and initial conditions) are assumed to be random Variables. By applying the Random Variable Transformation technique, the first probability density function, the mean and the variance functions, as well as confidence intervals associated with the solution of SIS-type epidemiological models, are determined. It is done under the general hypothesis that model random inputs have any joint probability density function. The distributions to describe the time until a given proportion of the population remains susceptible and infected are also determined. Finally, a probabilistic description of the so-called basic reproductive number is included. The theoretical results are applied to an illustrative example showing good fitting.
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probabilistic solution of random si type epidemiological models using the random Variable Transformation technique
Communications in Nonlinear Science and Numerical Simulation, 2015Co-Authors: M C Casaban, J C Cortes, J V Romero, M D RoselloAbstract:Abstract This paper presents a full probabilistic description of the solution of random SI-type epidemiological models which are based on nonlinear differential equations. This description consists of determining: the first probability density function of the solution in terms of the density functions of the diffusion coefficient and the initial condition, which are assumed to be independent random Variables; the expectation and variance functions of the solution as well as confidence intervals and, finally, the distribution of time until a given proportion of susceptibles remains in the population. The obtained formulas are general since they are valid regardless the probability distributions assigned to the random inputs. We also present a pair of illustrative examples including in one of them the application of the theoretical results to model the diffusion of a technology using real data.
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determining the first probability density function of linear random initial value problems by the random Variable Transformation rvt technique a comprehensive study
Abstract and Applied Analysis, 2014Co-Authors: M C Casaban, J C Cortes, J V Romero, M D RoselloAbstract:Deterministic differential equations are useful tools for mathematical modelling. The consideration of uncertainty into their formulation leads to random differential equations. Solving a random differential equation means computing not only its solution stochastic process but also its main statistical functions such as the expectation and standard deviation. The determination of its first probability density function provides a more complete probabilistic description of the solution stochastic process in each time instant. In this paper, one presents a comprehensive study to determinate the first probability density function to the solution of linear random initial value problems taking advantage of the so-called random Variable Transformation method. For the sake of clarity, the study has been split into thirteen cases depending on the way that randomness enters into the linear model. In most cases, the analysis includes the specification of the domain of the first probability density function of the solution stochastic process whose determination is a delicate issue. A strong point of the study is the presentation of a wide range of examples, at least one of each of the thirteen casuistries, where both standard and nonstandard probabilistic distributions are considered.
Charles J Geyer - One of the best experts on this subject based on the ideXlab platform.
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Variable Transformation to obtain geometric ergodicity in the random walk metropolis algorithm
Annals of Statistics, 2012Co-Authors: Leif T Johnson, Charles J GeyerAbstract:A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian analysis with conjugate priors of logistic and Poisson regression and of log-linear models for categorical data result in posterior distributions that are not super-exponentially light. We show how to apply the change-of-Variable formula for diffeomorphisms to obtain new densities that do satisfy the conditions for geometric ergodicity. Sampling the new Variable and mapping the results back to the old gives a geometrically ergodic sampler for the original Variable. This method of obtaining geometric ergodicity has very wide applicability.
