Large deviations for truncated heavy-tailed random variables: a boundary case

TL;DR

This paper studies the probability decay rates for sums of truncated heavy-tailed variables exceeding a threshold, focusing on the boundary case where the sum surpasses an integer multiple of the truncation point, using novel estimation techniques.

Contribution

It introduces a new approach for analyzing large deviations in the boundary case of truncated heavy-tailed sums, differing from previous methods for non-integer multiples.

Findings

Derived sharper estimates for boundary large deviations

Established decay rate formulas specific to the boundary case

Enhanced understanding of tail behavior in truncated heavy-tailed sums

Abstract

This paper investigates the decay rate of the probability that the row sum of a triangular array of truncated heavy tailed random variables is larger than an integer (k) times the truncating threshold, as both - the number of summands and the threshold go to infinity. The method of attack for this problem is significantly different from the one where k is not an integer, and requires much sharper estimates.