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Convergence of weighted averages of random variables revisited

Author: Nasrollah Etemadi
Journal: Proc. Amer. Math. Soc. 134 (2006), 2739-2744
MSC (2000): Primary 60F15
Published electronically: April 10, 2006
MathSciNet review: 2213754
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Abstract: We show that for a large class of positive weights including the ones that are eventually monotone decreasing and those that are eventually monotone increasing but vary regularly, if the averages of random variables converge in some sense, then their corresponding weighted averages also converge in the same sense. We will also replace the sufficient conditions in the fundamental result of Jamison, Pruitt, and Orey for i.i.d. random variables that make their work more transparent.

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Additional Information

Nasrollah Etemadi
Affiliation: Department of Mathematics, Statistics, & Computer Science, University of Illinois at Chicago, 322 Science & Engineering Offices (SEO) m/c 249, 851 S. Morgan Street, Chicago, Illinois 60607-7045

Keywords: Weighted averages, limit theorems, pairwise independence
Received by editor(s): December 6, 2004
Received by editor(s) in revised form: March 31, 2005, and April 14, 2005
Published electronically: April 10, 2006
Additional Notes: This work was partially supported by the Mahani Mathematical Research Center
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2006 American Mathematical Society

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