# Large deviations for infinite weighted sums of stretched exponential random variables

## TL;DR

This paper investigates the probabilities of rare large deviations in infinite weighted sums of independent random variables with stretched exponential tails, extending previous work to more general tail behaviors.

## Contribution

It generalizes existing large deviation results to infinite sums with stretched exponential tails, beyond finite exponential moments.

## Key findings

- Derived large deviation probabilities for infinite weighted sums with stretched exponential tails.
- Extended previous finite sum results to infinite sums in this tail regime.
- Provided new theoretical bounds for rare event probabilities in this setting.

## Abstract

We study the large deviation probabilities of infinite weighted sums of independent random variables that have stretched exponential tails. This generalizes Kiesel and Stadtm\"uller (2000), who study the same objects under the assumption of finite exponential moments, and Gantert et al.\ (2014), who study finite weighted sums with stretched exponential tails.