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

Frank Aurzada

doi:10.1016/j.spl.2008.02.007

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

Probability 2008-11-14 v2

Authors: Frank Aurzada

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Abstract

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 $0<q<1$ and $(X_n)$ are i.i.d. non-negative random variables. In particular, the asymptotics is shown to be the same for $S$ and $M$ in some cases.

Keywords

probability theory asymptotic distribution asymptotic analysis

Cite

@article{arxiv.0711.2576,
  title  = {A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights},
  author = {Frank Aurzada},
  journal= {arXiv preprint arXiv:0711.2576},
  year   = {2008}
}

Comments

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

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