  We present a new method to renormalize stochastic differential equations
subjected to multiplicative noise. The method is based on the widely used
concept of effective potential in high energy physics, and has already been
successfully applied to the renormalization of stochastic differential
equations subjected to additive noise. We derive a general formula for the
one-loop effective potential of a single ordinary stochastic differential
equation (with arbitrary interaction terms) subjected to multiplicative
Gaussian noise (provided the noise satisfies a certain normalization
condition). To illustrate the usefulness (and limitations) of the method, we
use the effective potential to renormalize a toy chemical model based on a
simplified Gray-Scott reaction. In particular, we use it to compute the scale
dependence of the toy model's parameters (in perturbation theory) when
subjected to a Gaussian power-law noise with short time correlations.
