应用数学2011，Vol.24Issue(3)：554-561,8.
线性过程关于矩的重对数律的精确率
Precise Rates in the Law of Iterated Logarithm for the Moment of Moving-average Processes
摘要
Abstract
In this paper,we discuss moving-average processXk = ∑∞ I=-∞ ai+kεi where {εi; - ∞<I<∞}is a doubly infinite sequence of I. I. D. Random variables with zero means and finite variances σ2 , {ai;- ∞<I<∞} is an absolutely summable sequence of real numbers.Set Sπ =∑n k=1 Xk,n≥1.Suppose E | ε1 |3 <∞, we prove that for any δ >- 1,lim ∈2δ+2 ∑∞ n=1 --(log logn)(∞) n3/2 log n E{| Sn |-∈τ √--2nlog log n}+=--√2τ √π(δ+1) (2δ+3)(F)(δ+2) ,∈↘0where τ2 =σ2 (∑∞ I=-∞ ai)2 and (F)(·) is a Gamma function.关键词
线性过程/完全矩收敛性/Berry-Esseen不等式Key words
Moving-average process/ Complete moment convergence/ Berry-Esseen ine-quality分类
数学引用本文复制引用
李云霞..线性过程关于矩的重对数律的精确率[J].应用数学,2011,24(3):554-561,8.基金项目
国家自然科学基金(10901136) （10901136）
