SIAM Journal on Numerical Analysis, Volume 62, Issue 3, Page 1021-1038, June 2024.
Abstract. Randomized quasi-Monte Carlo, via certain scramblings of digital nets, produces unbiased estimates of [math] with a variance that is [math] for any [math]. It also satisfies some nonasymptotic bounds where the variance is no larger than some [math] times the ordinary Monte Carlo variance. For scrambled Sobol’ points, this quantity [math] grows exponentially in [math]. For scrambled Faure points, [math] in any dimension, but those points are awkward to use for large [math]. This paper shows that certain scramblings of Halton sequences have gains below an explicit bound that is [math] but not [math] for any [math] as [math]. For [math], the upper bound on the gain coefficient is never larger than [math].

中文翻译：

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加扰 Halton 点的增益系数

SIAM 数值分析杂志，第 62 卷，第 3 期，第 1021-1038 页，2024 年 6 月
。摘要。随机准蒙特卡罗，通过数字网络的某些扰乱，产生[数学]的无偏估计，对于任何[数学]，其方差为[数学]。它还满足一些非渐近边界，其中方差不大于普通蒙特卡洛方差的某些[数学]倍。对于打乱的 Sobol' 点，这个数量 [math] 在 [math] 中呈指数增长。对于乱序的福尔点，任何维度的[数学]，但这些点很难用于大型[数学]。本文表明，Halton 序列的某些置乱具有低于显式界限的增益，该界限是 [math]，但对于任何 [math] 作为 [math] 而言不是 [math]。对于[math]，增益系数的上限永远不会大于[math]。