  In this article, we consider the problem of periodic homogenization of a
Feller process generated by a pseudo-differential operator, the so-called
L\'evy-type process. Under the assumptions that the generator has rapidly
periodically oscillating coefficients, and that it admits "small jumps" only
(that is, the jump kernel has finite second moment), we prove that the
appropriately centered and scaled process converges weakly to a Brownian motion
with covariance matrix given in terms of the coefficients of the generator. The
presented results generalize the classical and well-known results related to
periodic homogenization of a diffusion process.
