Casabán Bartual, MC.; Cortés López, JC.; Romero Bauset, JV.; Roselló Ferragud, MD. (2014). 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. 2014(248512):1-25. https://doi.org/10.1155/2014/248512
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/63028
Title:
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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
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Author:
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Casabán Bartual, Mª Consuelo
Cortés López, Juan Carlos
Romero Bauset, José Vicente
Roselló Ferragud, María Dolores
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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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 ...[+]
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.
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Subjects:
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Differential equations
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Copyrigths:
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Reconocimiento (by)
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Source:
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Abstract and Applied Analysis. (issn:
1085-3375
) (eissn:
1687-0409
)
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DOI:
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10.1155/2014/248512
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Publisher:
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Hindawi Publishing Corporation
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Publisher version:
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http://dx.doi.org/10.1155/2014/248512
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Project ID:
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info:eu-repo/grantAgreement/MICINN//DPI2010-20891-C02-01/ES/MODELIZACION Y METODOS NUMERICOS, ALEATORIOS Y DETERMINISTAS, PARA EL FILTRADO DE PARTICULAS DIESEL EN MOTORES DE COMBUSTION INTERNA SOBREALIMENTADOS/
info:eu-repo/grantAgreement/UPV//PAID-06-11-2070/
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Thanks:
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This work has been partially supported by the Ministerio de Economia y Competitividad under Grant no. DPI2010-20891-C02-01 and Universitat Politecnica de Valencia under Grant no. PAID06-11-2070.
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Type:
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Artículo
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