  We study the asymptotic limit, as $\varepsilon\searrow 0$, of solutions of
the stochastic Cahn-Hilliard equation: $$
  \partial_t u^\varepsilon=\Delta \left(-\varepsilon\Delta
u^\varepsilon+\frac{1}{\varepsilon}f(u^\varepsilon)\right)+\dot{\mathcal{W}}^\varepsilon_t,
\\ $$ where $\mathcal{W}^\varepsilon=\varepsilon^\sigma W$ or
$\mathcal{W}^\varepsilon=\varepsilon^\sigma W^\varepsilon$, $W$ is a $Q$-Wiener
process and $W^\varepsilon$ is smooth in time and converges to $W$ as
$\varepsilon\searrow 0$. In the case that
$\mathcal{W}^\varepsilon=\varepsilon^\sigma W$, we prove that for all
$\sigma>\frac{1}{2}$, the solution $u^\varepsilon$ converges to a weak solution
to an appropriately defined limit of the deterministic Cahn-Hilliard equation.
In radial symmetric case we prove that for all $\sigma\geq\frac{1}{2}$,
$u^\varepsilon$ converges to the deterministic Hele-Shaw model. In the case
that $\mathcal{W}^\varepsilon=\varepsilon^\sigma W^\varepsilon$, we prove that
for all $\sigma>0$, $u^\varepsilon$ converges to the weak solution to the
deterministic limit Cahn-Hilliard equation. In radial symmetric case we prove
that $u^\varepsilon$ converges to deterministic Hele-Shaw model when $\sigma>0$
and converges to a stochastic model related to stochastic Hele-Shaw model when
$\sigma=0$.
