Exponential Ergodicity of stochastic Burgers equations driven by $\alpha$-stable processes

TL;DR

This paper proves the exponential ergodicity and strong Feller property of stochastic Burgers equations driven by alpha-stable processes, extending understanding of their long-term behavior under non-Gaussian noise.

Contribution

It establishes exponential ergodicity for stochastic Burgers equations driven by alpha-stable noise, using novel truncation and derivative techniques for non-Gaussian SDEs.

Findings

Proves strong Feller property for the equations.

Establishes exponential ergodicity under alpha-stable noise.

Utilizes derivative formulas for non-Gaussian SDEs.

Abstract

In this work, we prove the strong Feller property and the exponential ergodicity of stochastic Burgers equations driven by $\alpha/2$-subordinated cylindrical Brownian motions with $\alpha\in(1,2)$. To prove the results, we truncate the nonlinearity and use the derivative formula for SDEs driven by $\alpha$-stable noises established in Zhang (arXiv:1204.2630v2).