Martingale approach to limit theorems for jump processes

We consider the weak convergence of laws of càdiàg processes determined by a sequence of operators with singularly perturbed terms. We study the problem in the martingale approach, which was formulated to establish weak limit theorems for continuous processes by Papanicolaou, Stroock and Varadhan. However, in this paper, limit processes are not necessarily continuous but càdiàg. In particular, we consider a homogenization problem of càdiàg processes in the framework of martingale problem.