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

Furlan, Marco; Gubinelli, Massimiliano (2018), Weak universality for a class of 3d stochastic reaction-diffusion models., Probability Theory and Related Fields. 10.1007/s00440-018-0849-6

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01615822
Date
2018
Journal name
Probability Theory and Related Fields
Publisher
Springer
Publication identifier
Metadata
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Author(s)
Furlan, Marco
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Gubinelli, Massimiliano
Hausdorff Center for Mathematics and Institute for Numerical Simulation - University of Bonn
Abstract (EN)
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.
Subjects / Keywords
weak universality; paracontrolled distributions; stochastic quantisation equation; Malliavin calculus; partial chaos expansion