On ergodic property of the solution to a L\'evy-driven SDE

TL;DR

This paper studies the ergodic behavior of solutions to Le9vy-driven stochastic differential equations with unbounded coefficients, focusing on convergence to invariant measures and providing examples.

Contribution

It offers new insights into the ergodic properties and convergence rates of Le9vy-driven SDEs with unbounded coefficients, which were less understood before.

Findings

Established conditions for ergodicity in total variation

Described the speed of convergence to invariant measures

Provided illustrative examples

Abstract

In this paper, we investigate ergodicity in total variation of the process $X_t$, related to a L\'evy-driven stochastic differential equation with unbounded coefficients, and describe the speed of convergence to the respective invariant measure. Some examples are provided.