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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
A Sampling and Transformation Approach to Solving Random Differential Equations

A Sampling and Transformation Approach to Solving Random Differential Equations

Roger, A. Erich
Air Force Institute of Technology (U S )

Paperback

General EducationGeneral Mathematics

ISBN10: 1249450063
ISBN13: 9781249450061
Publisher: Biblioscholar
Published: Sep 20 2012
Pages: 106
Weight: 0.35
Height: 0.22 Width: 6.14 Depth: 9.21
Language: English

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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