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J. Korean Math. Soc. 2008; 45(4): 993-1005

Printed July 1, 2008

Copyright © The Korean Mathematical Society.

Precise rates in the law of the logarithm for the moment convergence of i.i.d. random variables

Tian-Xiao Pang, Zheng-Yan Lin, Ye Jiang, and Kyo-Shin Hwang

Zhejiang University, Zhejiang University, Zhejiang University, Geongsang National University

Abstract

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Let $\{X, X_n; n\ge 1\}$ be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+\cdots+X_n$, $\displaystyle M_n=\max_{k\le n}|S_k|$, $n\ge 1$. Then we obtain that for any $-1 < b <\infty$.

Keywords: law of the logarithm, moment convergence, rate of convergence, strong approximation, i.i.d. random variables

MSC numbers: Primary 60F15; Secondary 60G50

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