The Experts below are selected from a list of 177756 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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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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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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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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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.
Jan Ramon - One of the best experts on this subject based on the ideXlab platform.
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A lower bound on the probability that a binomial Random Variable is exceeding its mean
Statistics & Probability Letters, 2016Co-Authors: Christos Pelekis, Jan RamonAbstract:We provide a lower bound on the probability that a binomial Random Variable is exceeding its mean. Our proof employs estimates on the mean absolute deviation and the tail conditional expectation of binomial Random Variables.
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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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.