Large deviation estimates related to arcsine laws for subordinators

TL;DR

This paper derives large deviation estimates for the behavior of subordinators near crossing times, extending the Dynkin--Lamperti theorem using regular variation and double Laplace transform techniques.

Contribution

It introduces new large deviation estimates related to the Dynkin--Lamperti theorem for subordinators, employing regular variation and double Laplace transform methods.

Findings

Established large deviation estimates for subordinators near crossing times

Extended the Dynkin--Lamperti theorem with new probabilistic bounds

Applied regular variation and double Laplace transform techniques

Abstract

We establish large deviation estimates related to the Dynkin--Lamperti theorem, which is a distributional limit theorem for the position of a subordinator immediately before it crosses a fixed level. Our approach relies on the theory of regular variation and the method of the double Laplace transform.