  This paper deals with homogenization of parabolic problems for integral
convolution type operators with a non-symmetric jump kernel in a periodic
elliptic medium. It is shown that the homogenization result holds in moving
coordinates. We determine the corresponding effective velocity and prove that
the limit operator is a second order parabolic operator with constant
coefficients. We also consider the behaviour of the effective velocity in the
case of small antisymmetric perturbations of a symmetric kernel.
