A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights

Details A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights

2007-11-16

arxiv.org/abs/0711.2576v2

Statistics & Probability Letters 78 (2008), 2300-2307

Mathematics

Probability

Revision, 13p, to appear in: Statist. Probab. Lett

Scientific paper

10.1016/j.spl.2008.02.007

We obtain some new results concerning the small deviation problem for
$S=\sum_n q^n X_n$ and $M=\sup_n q^n X_n$, where $0non-negative random variables. In particular, the asymptotics is shown to be
the same for $S$ and $M$ in some cases.

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