Exponential mixing for SPDEs driven by highly degenerate Lévy noises

Abstract

By modifying a coupling method developed by the third author with much more delicate analysis, we prove that a family of stochastic partial differential equations (SPDEs) driven by highly degenerate pure jump Lévy noises are exponential mixing. These pure jump Lévy noises include a finite dimensional $\alpha$-stable process with $\alpha \in (0,2)$.