Occupation times of generalized Ornstein-Uhlenbeck processes with two-sided exponential jumps

TL;DR

This paper derives formulas for the joint Laplace transform of an Ornstein-Uhlenbeck process with double exponential jumps and its occupation times, with potential extensions to more general Levy-driven processes.

Contribution

It provides a novel approach to compute occupation times for jump-diffusion Ornstein-Uhlenbeck processes, extending to Levy processes.

Findings

Formulas for joint Laplace transforms of the process and occupation times

Method can be extended to general Levy processes

Enhances understanding of jump-diffusion process behaviors

Abstract

For an Ornstein-Uhlenbeck process driven by a double exponential jump diffusion process, we obtain formulas for the joint Laplace transform of it and its occupation times. The approach used is remarkable and can be extended to investigate the occupation times of an Ornstein-Uhlenbeck process driven by a more general Levy process.