Homogenization of a class of integro-differential equations with L{\'e}vy operators

The periodic homogenization problem of integro-differential equations of the alpha stable L{'e}vy operators is studied in this paper. Thanking to the symmetry of the L{'e}vy density, we can use the method of the formal asymptotic expansion, to connect the problem to the ergodic cell problem. A rigorous proof is given by the perturbed test function’s method.