Moment Convergence Rates in the Law of the Logarithm for Dependent Sequences

Proceedings Mathematical Sciences

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 $𝜎^2=EX^2_1+2sum^∞_{k=2}EX_1X_k(0 < 𝜎 < ∞)$. In this paper, the exact convergence rates of a kind of weighted infinite series of $E{M_n-𝜎𝜀sqrt{nlog n}}_+$ and $E{|S_n|-𝜎𝜀sqrt{nlog n}}_+$ as $𝜀searrow 0$ and $E{𝜎𝜀sqrt{frac{𝜋^2 n}{8log n}}-M_n}_+$ as $𝜀earrow∞$ are obtained.

【 授权许可】

Unknown