  In this paper we consider the following stochastic partial differential
equation (SPDE) in the whole space:
  $du (t, x) = [a^{i j} (t, x) D_{i j} u(t, x)
  + f(u, t, x)]\, dt + \sum_{k = 1}^m g^k (u(t, x)) dw^k (t).$
  We prove the convergence of a Wong-Zakai type approximation scheme of the
above equation in the space
  $
  C^{\theta } ([0, T], H^{\gamma}_p (\mathbb{R}^d))
  $
  in probability, for some
  $
  \theta \in (0,1/2),
  \gamma \in (1, 2)$,
  and $p > 2$.
  We also prove a Stroock-Varadhan's type support theorem.
  To prove the results we combine V. Mackevicius ideas from his papers on
Wong-Zakai theorem and the support theorem for diffusion processes with N.V.
Krylov's $L_p$-theory of SPDEs.
