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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173992We 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.Revision, 13p, to appear in: Statist. Probab. LettProbability60G50, 60F99A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weightstext