Higher order approximations in arcsine laws for subordinators

TL;DR

This paper develops higher order approximation techniques for the distribution of killed subordinators near their first passage times, enhancing the classical arcsine law with detailed asymptotic expansions.

Contribution

It introduces higher order approximations in the arcsine law for subordinators and analyzes asymptotic expansions of potential densities for killed subordinators.

Findings

Higher order approximations improve the accuracy of the arcsine law.

Asymptotic expansions of potential densities are derived.

Results enhance understanding of subordinator behavior near first passage times.

Abstract

We establish higher order approximations in the Dynkin--Lamperti theorem, a limit theorem for the distribution of a killed subordinator immediately before its first passage time over a fixed level. For this purpose, we also study asymptotic expansions of potential densities for killed subordinators.