Moment convergence rates in the law of the logarithm for dependent sequences

被引：0
|
作者：
Ke-Ang Fu
Xiao-Rong Yang
机构：
[1] Zhejiang Gongshang University,School of Statistics and Mathematics
来源：
Proceedings - Mathematical Sciences | 2009年 / 119卷
关键词：
The law of the logarithm; Chung-type law of the logarithm; negative association; moment convergence; tail probability;
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学科分类号：
摘要：
Let {Xn; n ≥ 1} be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set Sn = Σk=1nXk, Mn = maxk≤n |Sk|, n ≥ 1. Suppose σ2 = EX12 + 2Σk=2∞ EX1Xk (0 < σ < ∞). In this paper, the exact convergence rates of a kind of weighted infinite series of E{Mn−σɛ√n log n}+ and E{|Sn| − σɛ√n log n}+ as ɛ ↘ 0 and E{σɛ√π2π/8logn − Mn}+ as ɛ ↗ ∞ are obtained.
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页码：387 / 400
页数：13
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