A Sampling and Transformation Approach to Solving Random Differential Equations - Brossura

Roger, A. Erich

Brossura

ISBN 10: 1249450063 ISBN 13: 9781249450061

Casa editrice: LIGHTNING SOURCE INC, 2012

Riassunto

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.

Dettagli dell'edizione

• Editore: LIGHTNING SOURCE INC
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1249450063
• ISBN 13: 9781249450061
• Rilegatura: Copertina flessibile
• Numero di pagine: 108
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile