Homogenization of non-autonomous evolution problems for convolution type operators in random media

We study homogenization problem for non-autonomous parabolic equations of the form ${\mathrm{\partial }}_{t}u=L(t)u$ with an integral convolution type operator $L(t)$ that has a non-symmetric jump kernel which is periodic in spatial variables and stationary random in time. We show that the homogenized equation is a SPDE with a finite dimensional multiplicative noise.