Weak universality for a class of 3d stochastic reaction-diffusion models.

Marco Furlan (1, 2) , Massimiliano Gubinelli (3, 4)

1 Université Paris Dauphine-PSL
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Instutute for Applied Mathematics [Bonn]
4 HCM - Hausdorff Center for Mathematics

We establish the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on a three dimensional periodic domain to the dynamic Phi^3_4 model within the framework of paracontrolled distributions. Our work extends previous results of Hairer and Xu to nonlinearities with a finite amount of smoothness (in particular C^9 is enough). We use the Malliavin calculus to perform a partial chaos expansion of the stochastic terms and control their L^p norms in terms of the graphs of the standard Phi^3_4 stochastic terms.

Mots clés: weak universality; paracontrolled distributions; stochastic quantisation equation; Malliavin calculus; partial chaos expansion

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Marco Furlan, Massimiliano Gubinelli. Weak universality for a class of 3d stochastic reaction-diffusion models.. 2017. ⟨hal-01615822⟩