[*bulk phase coexistence*]{}, [*i.e.*]{} for the value of $a=a_c$ for which in the absence of the wall the interface does not move on average, $\langle h \rangle$ diverges at all temperatures above certain wetting temperature, $T_W$, while for $a \not= a_c$ the thickness of the liquid film can be big, but finite (pinned interface). The temperature here is controlled by the parameter $b$, which vanishes linearly with the mean-field wetting temperature as $T-T_W$. Thus, on approaching coexistence for $T>T_W$ ($b>0$ at the mean-field level), $\langle h \rangle$ diverges as $\langle h \rangle \sim |a-a_c|^{\beta_h}$. This transition, termed [*complete wetting*]{}, is always continuous and the value of the $\beta_h$ exponent depends on the nature of the forces between the particles in the fluid phases and the wall. In this paper only short-range, exponentially decaying interactions between all the particles and the substrate (as described by Eq. (\[BKPZ\])) are considered.

The change of variables $n=\exp(-h)$ transforms Eq. (\[BKPZ\]) into the MN2 Langevin equation: $${\partial}_{t} n(x,t) =  
{\nabla}^{2} n - 2 {(\nabla n)^2 \over n}
-(a+1)n-bn^{p+1} +  n \eta,
\label{mnminus}$$ where for the sake of simplicity we have set $\lambda=D=\sigma=1$ and Ito calculus [@Ito] has been used (different coefficients for the Laplacian and 