Lim sup behavior of sums of geometrically weighted i.i.d. random variables

Andrew Rosalsky

Stochastic Processes and their Applications, 1981, vol. 11, issue 3, 297-300

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-->[infinity](b-1) [Sigma]nj=1b1Yj[+45 degree rule]bn+1=L, almost certainly, where L is the essential supremum of Y1.

Date: 1981
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