Limit Theorems for Super-heavy Tailed Random Variables with Truncation: Application to the Super-petersburg Game

Abstract

Motivated by the super-Petersburg game, we consider the super-heavy tailed independent and identically distributed (iid) random variables whose tail are characterized by slow variation. This article explores strong laws of large numbers and central limit theorems for a class of super-heavy tailed random variables with two types of truncations, respectively. We apply our results to the logPareto distributions and the super-Petersburg distributions.