A general large deviation result for partial sums of i.i.d. super-heavy tailed random variables

Abstract

In this paper, a general large deviation result for partial sums of independent and identically distributed random variables with super-heavy tailed distribution is established. Our main result extends in particular the results of Stoica (2008) and Nakata (2022). The symmetrization technique, one of Lévy’s inequalities, and two preliminary results on slowly and regularly varying functions are paramount in the proof of our main result.