©2020 American Physical SocietyGagnon, Jean SébastienHochberg, DavidPérez Mercader, JuanUnidad de Excelencia Científica María de Maeztu Centro de Astrobiología del Instituto Nacional de Técnica Aeroespacial y CSIC, MDM-2017-07372022-02-072022-02-072020-12-23Physical Review E 102 (6)2470-0053https://journals.aps.org/pre/abstract/10.1103/PhysRevE.102.062142http://hdl.handle.net/20.500.12666/477We present a 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.engPolímeros dirigidos., SimulaciónDirected Polymers., Simulationinfo:eu-repo/semantics/article10.1103/PhysRevE.102.062142info:eu-repo/semantics/restrictedAccess