Bull. Korean Math. Soc. 2010; 47(6): 1139-1153
Printed November 1, 2010
https://doi.org/10.4134/BKMS.2010.47.6.1139
Copyright © The Korean Mathematical Society.
Yong-Kab Choi and Hee-Jin Moon
Gyeongsang National University, Gyeongsang National University
Let $\{X_j,\, j \ge 1\}$ be a strictly stationary $\phi$-mixing sequence of non-degenerate random variables with ${\bf E} X_1 =0$. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence $\{X_j\}$ under the condition that $L(x):={\bf E} X_1^2I\{|X_1|\le x\}\ \text{is a slowly varying function at $\infty$}$, without any higher moment conditions.
Keywords: self-normalized random variables, invariance principle, central limit theorem, mixing sequence
MSC numbers: Primary 60F15, 60F17
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