Occupation times of intervals until last passage times for spectrally negative Levy processes

TL;DR

This paper derives explicit formulas for the joint Laplace transforms of occupation times and last passage times in spectrally negative Levy processes, advancing understanding of their probabilistic structure.

Contribution

It introduces new analytical identities and applies dual arguments to obtain explicit formulas for occupation and last passage times in spectrally negative Levy processes.

Findings

Explicit formulas for joint Laplace transforms of occupation and last passage times.

New analytical identities derived from prior work.

Application of dual arguments to obtain results.

Abstract

In this paper, we derive the joint Laplace transforms of occupation times until its last passage times as well as its positions. Motivated by Baurdoux [2], the last times before an independent exponential variable are studied. By applying dual arguments, explicit formulas are derived in terms of new analytical identities from Loeffen et al. [12].