The almost sure local central limit theorem for products of partial sums under negative association

Journal of Inequalities and Applications

Yuanying Jiang¹  Qunying Wu¹ 

[1] College of Science, Guilin University of Technology;

关键词: Negative association;    Products of partial sums;    Almost sure local central limit theorem;    Almost sure global central limit theorem;   

DOI  :  10.1186/s13660-018-1875-8

来源: DOAJ

【 摘 要 】

Abstract Let {Xn,n≥1} $\{X_{n}, n\geq1\}$ be a strictly stationary negatively associated sequence of positive random variables with EX1=μ>0 $\mathrm{E}X_{1}=\mu>0$ and Var(X1)=σ2<∞ $\operatorname{Var}(X_{1})=\sigma^{2}<\infty$. Denote Sn=∑i=1nXi,pk=P(ak≤(∏j=1kSj/(k!μk))1/(γσ1k)0 $\sigma_{1}^{2}=1+\frac{1}{\sigma^{2}}\sum_{j=2}^{\infty}\operatorname{Cov}(X_{1},X_{j})>0$.

【 授权许可】

Unknown