An almost sure central limit theorem for self-normalized products of sums of i.i.d. random variables

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:376

Article

Zhang, Yong¹  Yang, Xiao-Yun¹ 

[1] Jilin Univ, Coll Math, Changchun 130012, Peoples R China

关键词: Almost sure central limit theorem;    Self-normalized;    Products of sums;    Domain of attraction of the normal law;   

DOI  :  10.1016/j.jmaa.2010.10.021

来源: Elsevier

【 摘 要 】

Let X, X-1, X-2, ... be a sequence of independent and identically distributed positive random variables with EX = mu > 0. In this paper we show that the almost sure central limit theorem for self-normalized products of sums holds only under the assumptions that X belongs to the domain of attraction of the normal law. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free