On the Discrepancy of Random Walks on the Circle

A. Bazarova, I. Berkes, M. Raseta
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引用次数: 2

Abstract

Abstract Let X1,X2,... be i.i.d. absolutely continuous random variables, let Sk=∑j=1kXj {S_k} = \sum\nolimits_{j = 1}^k {{X_j}} (mod 1) and let D*N denote the star discrepancy of the sequence (Sk)1≤k≤N. We determine the limit distribution of ND N* \sqrt N D_N^* and the weak limit of the sequence N(FN(t)-t) \sqrt N \left( {{F_N}(t) - t} \right) in the Skorohod space D[0, 1], where FN (t) denotes the empirical distribution function of the sequence (Sk)1≤k≤N.
关于圆上随机游动的不一致性
设X1,X2,…令Sk=∑j=1kXj {S_k} = \sum\nolimits _j =1{ ^k }X_j{{ (mod 1),令D*N表示序列(Sk)1≤k≤N的星差。我们确定了ND N* }}\sqrt N D_N^*的极限分布和序列N(FN(t)-t) \sqrt N \left ({{F_N}(t) -t }\right)在Skorohod空间D[0, 1]中的弱极限,其中FN(t)表示序列(Sk)1≤k≤N的经验分布函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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