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

Large deviations for infinite weighted sums of stretched exponential random variables