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

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).