Homogenization of Levy-type operators with oscillating coefficients

The paper deals with homogenization of Levy-type operators with rapidly oscillating coefficients. We consider cases of periodic and random statistically homogeneous micro-structures and show that in the limit we obtain a Levy-operator. In the periodic case we study both symmetric and non-symmetric kernels whereas in the random case we only investigate symmetric kernels. We also address a nonlinear version of this homogenization problem.