J. Korean Math. Soc. 2008; 45(2): 355-365
Printed March 1, 2008
Copyright © The Korean Mathematical Society.
Tae-Sung Kim, Mi-Hwa Ko, and Yong-Kab Choi
WonKwang University, WonKwang University, Gyeongsang National University
Let $\{Y_i ;-\infty < i <\infty\}$ be a doubly infinite sequence of identically distributed and $\phi$-mixing random variables with
zero means and finite variances and $\{a_i ;-\infty < i <\infty\}$ an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of $\{\sum_{k=1}^n \sum_{i=-\infty}^\infty a_{i+k} Y_i/n^{1/p} ; n \geq 1\}$ under some suitable conditions.
Keywords: moving average process, complete moment convergence, $\phi$-mixing
MSC numbers: 60G50, 60F15
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