Tail probabilities of St. Petersburg sums, trimmed sums, and their limit

Abstract

We provide exact asymptotics for the tail probabilities $\mathbb{P}\{S_{n,r}>x\}$ as $x\to \infty$, for fix $n$, where $S_{n,r}$ is the $r$-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that although the St. Petersburg distribution is only O-subexponential, the subexponential property almost holds. We also determine the exact tail behavior of the $r$-trimmed limits.

24 pages, 2 figures