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The periodic homogenization problem of integro-differential equations of thealpha stable L{\'e}vy operators is studied in this paper. Thanking to thesymmetry of the L{\'e}vy density, we can use the method of the formalasymptotic expansion, to connect the problem to the ergodic cell problem. Arigorous proof is given by the perturbed test function's method.

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