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A Sampling and Transformation Approach to Solving Random Differential Equations - Tapa blanda

Roger, A. Erich

 
9781249450061: A Sampling and Transformation Approach to Solving Random Differential Equations
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ISBN 10: 1249450063 ISBN 13: 9781249450061
Editorial: BiblioScholar, 2012

Sinopsis

This research explores an innovative sampling method used to conduct uncertainty analysis on a system with one random input.Given the distribution of the random input, X, we seek to find the distribution of the output random variable Y. When the functional form of the transformationY=g(X) is not explicitly known, complicated procedures, such as stochastic projection or Monte Carlo simulation must be employed. The main focus of thisresearch is determining the distribution of the random variable Y=g(X) where g(X) is the solution to an ordinary differential equation and X is a randomparameter. Here, y=g(X) is approximated by constructing a sample {Xi, Yi} where the Xi are not random, but chosen to be evenly spaced on the interval [a, b]and Yi=g(Xi). Using this data, an efficient approximation "(X) ~ g(X) is constructed. Then the transformation method, in conjunction with "(X), is used tofind the probability density function of the random variable Y. This uniform sampling method and transformation method will be compared to the stochasticprojection and Monte Carlo methods currently being used in uncertainty analysis. It will be demonstrated, through several examples, that the proposed uniformsampling method and transformation method can work faster and more efficiently than the methods mentioned.

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Reseña del editor

This research explores an innovative sampling method used to conduct uncertainty analysis on a system with one random input.Given the distribution of the random input, X, we seek to find the distribution of the output random variable Y. When the functional form of the transformationY=g(X) is not explicitly known, complicated procedures, such as stochastic projection or Monte Carlo simulation must be employed. The main focus of thisresearch is determining the distribution of the random variable Y=g(X) where g(X) is the solution to an ordinary differential equation and X is a randomparameter. Here, y=g(X) is approximated by constructing a sample {Xi, Yi} where the Xi are not random, but chosen to be evenly spaced on the interval [a, b]and Yi=g(Xi). Using this data, an efficient approximation "(X) ~ g(X) is constructed. Then the transformation method, in conjunction with "(X), is used tofind the probability density function of the random variable Y. This uniform sampling method and transformation method will be compared to the stochasticprojection and Monte Carlo methods currently being used in uncertainty analysis. It will be demonstrated, through several examples, that the proposed uniformsampling method and transformation method can work faster and more efficiently than the methods mentioned.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
BiblioScholar
Año de publicación
2012
Idioma
Inglés
ISBN 10 
1249450063
ISBN 13 
9781249450061
Encuadernación
Tapa blanda
Número de páginas
108
Contacto del fabricante
no disponible
Persona responsable
no disponible