# Uniqueness of martingale problem for Levy type operator

Consider the following Levy type operator: $$L_t\varphi(x)=\int_{R^d}\big[\varphi(x+z)-\varphi(x)-1_{|z|\leq 1}z\cdot\nabla\varphi(x)\big]\kappa(x,z)\nu(dz),\quad\forall \varphi\in C_c^2(R^d),$$ where $$\nu$$ is an symmetric Levy measure, $$\kappa(\cdot,z)\in C^\infty(R^d)$$ (smooth in $$x$$, but maybe degenerate and unbounded), and for each $$x$$, $$\int_{R^d}(|z|^2\wedge1)\kappa(x,z)\nu(dz)<\infty.$$ Then, is the martingale problem for $$L$$ has a unique solution? I think the conclusion should be true, since the coefficient is smooth, but I can not find a reference. Thanks for the help.