Pseudo-random sequences, quasi-random sequences for simulation

点击翻译按钮获取中文摘要

Mathematical models arising in many applied sciences are too complex to solve directly, and so must be solved using a numerical approximation. Unfortunately, as the number of variables in a problem increases, most numerical approximation techniques become ineffective, since the time required to reach a prescribed level of accuracy increases exponentially. Monte Carlo methods are a class of sampling techniques in which one attempts to solve a problem by generating suitable random numbers and observing the fraction of the numbers obeying some property. They seem to perform well for moderate to high-dimensional problems. Many Monte Carlo problems ultimately require non-uniform samples. The primary focus of this research is finding new methods to generate multivariate non-uniform pseudo-random and quasi-random samples with properties desirable for use with Monte Carlo simulations.