A Law of the Iterated Logarithm for Random Geometric Series
Bovier, Anton ; Picco, Pierre
Ann. Probab., Tome 21 (1993) no. 4, p. 168-184 / Harvested from Project Euclid
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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 $\lbrack-1, 1\rbrack$.
Publié le : 1993-01-14
Classification:  Law of the iterated logarithm,  Hartman-Wintner condition,  60F05,  60F15 
@article{1176989399,
     author = {Bovier, Anton and Picco, Pierre},
     title = {A Law of the Iterated Logarithm for Random Geometric Series},
     journal = {Ann. Probab.},
     volume = {21},
     number = {4},
     year = {1993},
     pages = { 168-184},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989399}
}

Bovier, Anton; Picco, Pierre. A Law of the Iterated Logarithm for Random Geometric Series. Ann. Probab., Tome 21 (1993) no. 4, pp.  168-184. http://gdmltest.u-ga.fr/item/1176989399/