An incompressible fluid is assumed to satisfy the time‐dependent Stokes equations in a porous medium. The porous medium is modeled by a bounded domain in
$R^n$
that is perforated for each ε > 0 by ε‐dilations of a subset of
$R^n$
arising from a family of stochastic processes which generalize the homogeneous random fields. The solution of the Stokes equations on these perforated domains is homogenized as ε → 0 by means of stochastic two‐scale convergence in the mean, and the homogenized limit is shown to satisfy a two‐pressure Stokes system containing both deterministic and stochastic derivatives and a Darcy‐type law with memory which generalizes the Darcy law obtained for fluid flow in periodically perforated porous media.
