  The asymptotic expansion method is generalized from the periodic setting to
stationary ergodic stochastic geometries. This will demonstrate that results
from periodic asymptotic expansion also apply to non-periodic structures of a
certain class. In particular, the article adresses non-mathematicians who are
familiar with asymptotic expansion and aims at introducing them to stochastic
homogenization in a simple way. The basic ideas of the generalization can be
formulated in simple terms, which is basically due to recent advances in
mathematical stochastic homogenization. After a short and formal introduction
of stochastic geometry, calculations in the stochastic case will be formulated
in a way that they will not look different from the periodic setting. To
demonstrate that, the method will be applied to diffusion with and without
microscopic nonlinear boundary conditions and to porous media flow. Some
examples of stochastic geometries will be given.
