# Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments

## TL;DR

This paper investigates the tail behavior of the distribution of the area under positive excursions of a heavy-tailed, negatively drifting random walk, providing asymptotic results for tail probabilities.

## Contribution

It derives the asymptotics of tail probabilities for the area under excursions of a heavy-tailed random walk with negative drift, a novel analysis in this context.

## Key findings

- Established asymptotic formulas for tail probabilities
- Characterized the influence of heavy tails on the area distribution
- Extended understanding of random walk excursion areas with heavy-tailed increments

## Abstract

We study tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and heavy-tailed increments. We determine the asymptotics for tail probabilities for the area.