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We consider SDEs driven by multiplicative pure jump L\'{e}vy noises, whereL\'evy processes are not necessarily comparable to $\alpha$-stable-likeprocesses. By assuming that the SDE has a unique solution, we obtain gradientestimates of the associated semigroup when the drift term is locally H\"{o}ldercontinuous, and we establish the ergodicity of the process both in the$L^1$-Wasserstein distance and the total variation, when the coefficients aredissipative for large distances. The proof is based on a new explicit Markovcoupling for SDEs driven by multiplicative pure jump L\'{e}vy noises, which isderived for the first time in this paper.

Gradient Estimates and Ergodicity for SDEs Driven by Multiplicative L\'{e}vy Noises via Coupling