Long time behavior of Levy-driven Ornstein-Uhlenbeck process with regime-switchin

TL;DR

This paper analyzes the long-term behavior of Levy-driven Ornstein-Uhlenbeck processes with regime-switching, providing criteria for transience and recurrence, and highlighting how Levy noise and regime-switching influence the heavy-tailed stationary distribution.

Contribution

It offers explicit criteria for transience and recurrence and clarifies the distinct roles of Levy measure and regime-switching in stationary distribution properties.

Findings

Criteria for transience and recurrence are established.

Heavy-tailed stationary distributions can arise due to Levy noise and regime-switching.

The roles of Levy measure and regime-switching are distinctly characterized.

Abstract

In this work we investigate the long time behavior of the Ornstein-Uhlenbeck process driven by Levy noise with regime-switching. We provide explicit criteria on the transience and recurrence of this process. Contrasted with the Ornstein-Uhlenbeck process driven simply by Brownian motion, whose stationary distribution must be light-tailed, both the jumps caused by the Levy noise and regime-switching described by Markov chain can derive the heavy-tailed property of the stationary distribution. In this work, the different role played by Levy measure and regime-switching process is clearly characterized.