Strong approximation theorems for geometrically weighted random series and their applications

• 成果类型: Article
• 署名作者: Zhang, LX
• 署名单位: Zhejiang University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1023481105
• 发表日期: 1997
• 页码: 1621-1635
• 关键词: random-variables; iterated logarithm; partial sums; LAW

摘要

Let (X-n; n greater than or equal to 0) be a sequence of random variables. We consider its geometrically weighted series xi(beta) = Sigma(n=0)(infinity) beta(n) X-n for 0 < beta < 1. This paper proves that xi(beta) can be approximated by Sigma(n=0)(infinity) beta(n) Y-n under some suitable conditions, where (Y-n; n greater than or equal to 0) is a sequence of independent normal random variables. Applications to the law of the iterated logarithm for xi(beta) are also discussed.