On complete convergence for weighted sums of i.i.d. random variables with application to moving average processes
Bull. Korean Math. Soc. 2009 Vol. 46, No. 4, 617-626
https://doi.org/10.4134/BKMS.2009.46.4.617
Printed July 1, 2009
Soo Hak Sung
Pai Chai University
Abstract : Let $\{Y_i, -\infty < i < \infty \}$ be a doubly infinite sequence of i.i.d. random variables with $E|Y_1|<\infty,$ $\{a_{ni}, -\infty < i < \infty, n \ge 1 \}$ an array of real numbers. Under some conditions on $\{a_{ni}\},$ we obtain necessary and sufficient conditions for $\sum_{n=1}^\infty \frac{1}{n}P(|\sum_{i=-\infty}^\infty a_{ni}(Y_i-EY_i)|>n\epsilon)<\infty.$ We examine whether the result of Spitzer [11] holds for the moving average process, and give a partial solution.
Keywords : complete convergence, moving average process, weighted sums, sums of independent random variables
MSC numbers : 60F15, 60G50
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