Gagnon Jean-Sébastien, Hochberg David, Pérez-Mercader Juan
Department of Physics, Norwich University, Northfield, Vermont 05663, USA.
Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
Phys Rev E. 2020 Dec;102(6-1):062142. doi: 10.1103/PhysRevE.102.062142.
We 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.
