Exponential mixing for SDEs forced by degenerate Levy noises

Abstract: We modify the coupling method established in [22, 20] and develop a technique to prove the exponential mixing of a 2D stochastic system forced by degenerate Levy noises. In particular, these Levy noises include $\alpha$-stable noises (0 < $\alpha$ < 2). Thanks to the stimulating discussion [14], this technique is promising to study the exponential mixing problem of SPDEs driven by degenerate symmetric $\alpha$-stable noises.