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We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Levy process. The diffusion coefficient is only locally Lipschitz and bounded. Under a mild condition on the large jumps of the Levy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest. Subject Classification (MSC2000): 34K50, 60G48

Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations