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January, 1993 A Law of the Iterated Logarithm for Random Geometric Series
Anton Bovier, Pierre Picco
Ann. Probab. 21(1): 168-184 (January, 1993). DOI: 10.1214/aop/1176989399


We consider the random variables $\xi(\beta) = \sum^\infty_{n = 0}\beta^n\varepsilon_n$ for $\beta < 1$. We prove that if the $\varepsilon_n$ are i.i.d. random variables with mean zero and variance 1, then a law of the iterated logarithm holds in the sense that the cluster set of $\frac{\sqrt{1 - \beta^2}}{2\log\log(1/(1 - \beta^2))}\xi(\beta),$ when $\beta$ converges to one, is the interval $\lbrack-1, 1\rbrack$.


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Anton Bovier. Pierre Picco. "A Law of the Iterated Logarithm for Random Geometric Series." Ann. Probab. 21 (1) 168 - 184, January, 1993.


Published: January, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0770.60029
MathSciNet: MR1207221
Digital Object Identifier: 10.1214/aop/1176989399

Primary: 60F05
Secondary: 60F15

Keywords: Hartman-Wintner condition , Law of the iterated logarithm

Rights: Copyright © 1993 Institute of Mathematical Statistics

Vol.21 • No. 1 • January, 1993
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