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

Exponential mixing for SDEs forced by degenerate Levy noises