Ordinary Differential Equations and Applied Dynamics Commons^™

A Sampling And Transformation Approach To Solving Random Differential Equations, Roger A. Erich

Theses and Dissertations

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 transformation Y=g(X) is not explicitly known, complicated procedures, such as stochastic projection or Monte Carlo simulation must be employed. The main focus of this research 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 random parameter. Here, y=g(X) is approximated by …