Abstract
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0} be a sequence of negatively associated random variables. we consider its geometrically weighted series ξ(β)=∑
1.
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doi:10.1016/0304-4149(81)90031-4 
Copyright © 1981 Published by Elsevier Science B.V. All rights reserved.
Short communication
Lim sup behavior of sums of geometrically weighted i.i.d. random variables
Received 16 March 1979;
revised 15 April 1980.
Available online 26 March 2002.
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Abstract
Geometrically weighted i.i.d. random variables {Yn} which are bounded above are shown to exhibit iterated logarithm type behavior. Specifically, if b > 1 and if the lower tail of the distribution of Y1 approaches 0 fast enough, then lim supn→∞(b−1) Σnj=1b1Yj
bn+1=L, almost certainly, where L is the essential supremum of Y1.
Mathematical subject codes: Primary 60F15; Law of the iterated logarithm; weighted i.i.d. random variables; essential supremum; geometric weights; iterated logarithm type behavior
