An extension of a theorem of Mikosch

详细信息    查看全文

• 作者：Yuye Zou^a ; Xiangdong Liu^b ; ^{tliuxd@jnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60F15 ; 60G50
• 刊名：Statistics & Probability Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：120
• 期：Complete
• 页码：81-86
• 全文大小：383 K

文摘

Let 0<α≤2$0<\alpha \le 2$. Let N^d${\mathbb{N}}^d$ be the d$d$-dimensional lattice equipped with the coordinate-wise partial order ≤$\le$, where d≥1$d\ge 1$ is a fixed integer. For $n=(n_1,\dots ,n_d)\in {\mathbb{N}}^d$, define $\left|n\right|={\prod }_{i=1}^d{n}_i$. Let $\{X,X_n;n\in {\mathbb{N}}^d\}$ be a field of independent and identically distributed real-valued random variables. Set $S_n={\sum }_{k\le n}{X}_k$, $n\in {\mathbb{N}}^d$ and write $logx={log}_e(e\vee x),x\ge 0$. This note is devoted to an extension of a strong limit theorem of Mikosch (1984). By applying an idea of Li and Chen (2014) and the classical Marcinkiewicz–Zygmund strong law of large numbers for random fields, we obtain necessary and sufficient conditions for