Renormalization Group and Stochastic PDE's

Abstract

We develop a Renormalization Group (RG) approach to the study of existence and uniqueness of solutions to stochastic partial differential equations driven by space-time white noise. As an example we prove well-posedness and independence of regularization for the ${\varphi }^4$ model in three dimensions recently studied by Hairer. Our method is "Wilsonian": the RG allows to construct effective equations on successive space time scales. Renormalization is needed to control the parameters in these equations. In particular no theory of multiplication of distributions enters our approach.

arXiv comment31 pages. Revised version with comments and references added and Lemma 10 corrected and absorbed to Proposition 11

References in corpus (1)

• Generalized PDE estimates for KPZ equations through Hamilton-Jacobi-Bellman formalism

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