  We consider the homogenization problem for the stochastic porous-medium type
equation $\p_{t} u^\epsilon =\Delta
f\left(T\left(\frac{x}{\ep}\right)\om,u^\ep\right)$, with a well-prepared
initial datum, where $f(T(y)\om,u)$ is a stationary process, increasing in $u$,
on a given probability space $(\Om, \mathcal{F}, \mu)$ endowed with an ergodic
dynamical system $\{T(y)\,:\,y\in\R^N\}$. Differently from the previous
literature \cite{afs,fs}, here we do not assume $\Om$ compact. We first show
that the weak solution $u^\ep$ satisfies a kinetic formulation of the equation,
then we exploit the theory of
  "stochastically two-scale convergence in the mean" developed in \cite{bmw} to
show convergence of the kinetic solution to the kinetic solution of an
homogenized problem of the form
  $\p_{t} \overline{u} - \Delta \overline{f}(\overline{u})=0$.
  The homogenization result for the weak solutions then follows.
