Exponential ergodicity for non-Lipschitz multivalued stochastic differential equations with Lévy jumps

Abstract

We study the exponential ergodicity of diffusions generated by a multivalued stochastic differential equation with Lévy jumps when the coefficients are non-Lipschitz continuous by proving that the transition semigroup is strongly Feller and irreducible, and that it admits a unique invariant measure. This is obtained through an [Formula: see text]-convergence result, Girsanov’s theorem, coupling method combined and a stopping argument.