The martingale problem for a class of stable-like processes

Let α∈(0,2)α∈(0,2) and consider the operator Lf(x)=∫[f(x+h)−f(x)−1(|h|≤1)∇f(x)⋅h]A(x,h)|h|d+αdh for f∈C2(Rd)f∈C2(Rd), where the ∇f(x)⋅h∇f(x)⋅h term is omitted if α<1α<1. We consider the martingale problem corresponding to the operator LL and under mild conditions on the function AA prove that there exists a unique solution.