On the exponential ergodicity for L\'{e}vy driven Ornstein-Uhlenbeck processes

TL;DR

This paper proves the ergodicity and exponential ergodicity of Lévy driven Ornstein-Uhlenbeck processes using explicit coupling methods, advancing understanding of their long-term behavior.

Contribution

It introduces a novel approach to establish ergodicity for Lévy driven Ornstein-Uhlenbeck processes through explicit coupling techniques.

Findings

Proves ergodicity of Lévy driven Ornstein-Uhlenbeck processes.

Establishes exponential rate of convergence to equilibrium.

Provides explicit coupling construction for these processes.

Abstract

Based on the explicit coupling property, the ergodicity and the exponential ergodicity of L\'{e}vy driven Ornstein-Uhlenbeck processes are established.