From averaging to homogenization in cellular flows - an exact   description of the transition
  We consider a two-parameter averaging-homogenization type elliptic problem together with the stochastic representation of the solution. A limit theorem is derived for the corresponding diffusion process and a precise description of the two-parameter limit behavior for the solution of the PDE is obtained. 
Martin Hairer and Leonid Koralov and Zsolt Pajor-Gyulai
math.PR math.AP