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
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
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd