Volume Dispersion of Point Sets and Quasi-Monte Carlo Methods

摘要

Measures of irregularity of a point set or sequence, such as discrepancy and dispersion, play a central role in quasi-Monte Carlo methods. In this paper, we introduce and study a new measure of irregularity, called volume dispersion. It is a measure of deviation of point sets from the uniform distribution. We then generalize the concept of volume dispersion to more general cases as measures of representation of point sets for general probability distributions. Various relations among these measures and the traditional discrepancy and dispersion are investigated.