Asymptotic behavior of average Lp-discrepancies
We investigate the limit behavior of the average L-p-B-discrepancy for 0 < p < infinity if the number of sample points tends to infinity. We adopt a recent result of Steinerberger and give asymptotic expressions for several types of discrepancy functions studied in the literature. This also leads to a new proof for the average L-p-star discrepancy. Our methods are probabilistic in nature. Furthermore, we employ symmetrization techniques to obtain estimates for arbitrary p. (c) 2012 Elsevier Inc. All rights reserved.
star discrepancy average discrepancy uniform distribution theory quasi-monte carlo methods