Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences

Authors:	Mi Chenjing

Affiliation:	(1) Dept. of Math, Zhejiang Univ., 310028 Hangzhou, China

Abstract:	Let {X _i;i≥1} be a strictly stationary sequence of associated random variables with mean zero and let $sigma ^2 = EX_1^2 + 2sumnolimits_{j = 2}^infty {EX_1 X_j }$ with O<σ ²<∞. Set $S_n = sumnolimits_{i = 1}^n {X_i }$ , the precise asymptotics for $sumnolimits_{n geqslant 1} {n^{frac{r}{p} - 2} } Pleft( {left\| {S_n } right\| geqslant varepsilon n^{frac{1}{p}} } right),sumnolimits_{n geqslant 1} {frac{1}{n}P} left( {left\| {S_n } right\| geqslant varepsilon n^{frac{1}{p}} } right)$ and $sumnolimits_{n geqslant 1} {frac{{left( {log n} right)^delta }}{n}} Pleft( {left\| {S_n } right\| geqslant varepsilon sqrt {nlogn} } right)$ as are established.

Keywords:	complete convergence associated random variables Baum-Katz law precise asymptotics.
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