Abstract
The stochastic two-scale convergence method, recently developed in an article by Zhikov and Piatnitskii [Izv. Math. 70(1) (2006), 19–67] is extended to arbitrary probability spaces and is now based on the theory of stochastic geometry instead of random measures. It will be shown that former results on stochastic and periodic two-scale convergence fit into the new approach in a natural way. These results will be applied to functions with jumps on (n−1)-dimensional manifolds, in particular to a homogenization problem of heat transfer through a composite material or polycrystal.