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 | References | Similar Articles | Additional Information

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

Email:
Etemadi@uic.edu

DOI:
https://doi.org/10.1090/S0002-9939-06-08296-7

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