期刊论文详细信息
Proceedings Mathematical Sciences | |
Moment Convergence Rates in the Law of the Logarithm for Dependent Sequences | |
Xiao-Rong Yang1  Ke-Ang Fu2  | |
[1] $$;School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 0 0, China$$ | |
关键词: The law of the logarithm; Chung-type law of the logarithm; negative association; moment convergence; tail probability.; | |
DOI : | |
学科分类:数学(综合) | |
来源: Indian Academy of Sciences | |
【 摘 要 】
Let ${X_n;n≥ 1}$ be a strictly stationary sequence of negatively associated random variables with mean zero and finite variance. Set $S_n=sum^n_{k=1}X_k,M_n=max_{k≤ n}|S_k|,n≥ 1$. Suppose $ðœŽ^2=EX^2_1+2sum^∞_{k=2}EX_1X_k(0 < 𜎠< ∞)$. In this paper, the exact convergence rates of a kind of weighted infinite series of $E{M_n-ðœŽðœ€sqrt{nlog n}}_+$ and $E{|S_n|-ðœŽðœ€sqrt{nlog n}}_+$ as $ðœ€searrow 0$ and $E{ðœŽðœ€sqrt{frac{ðœ‹^2 n}{8log n}}-M_n}_+$ as $ðœ€earrow∞$ are obtained.
【 授权许可】
Unknown
【 预 览 】
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