  We study the role of multiplicative stochastic processes in the description
of the dynamics of an order parameter near a critical point. We study
equilibrium, as well as, out-of-equilibrium properties. By means of a
functional formalism, we built the Dynamical Renormalization Group equations
for a real scalar order parameter with $Z_2$ symmetry, driven by a class o
multiplicative stochastic processes with the same symmetry. We have computed
the flux diagram, using a controlled $\epsilon$-expansion, up to order
$\epsilon^2$. We have found that, for dimensions $d=4-\epsilon$, the additive
dynamic fixed point is unstable. The flux runs to a {\em multiplicative fixed
point} driven by a diffusion function $G(\phi)=1+g^*\phi^2({\bf x})/2$, where
$\phi$ is the order parameter and $g^*=\epsilon^2/18$ is the fixed point value
of the multiplicative noise coupling constant. We show that, even though the
position of the fixed point depends on the stochastic prescription, the
critical exponents do not. Therefore, different dynamics driven by different
stochastic prescriptions (such as It\^o, Stratonovich, anti-It\^o and so on)
are in the same universality class.
