Year: 2014
Type: preprint
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 $ϕ^4$ 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.
Source: arXiv (Cornell University)
Author: Kupiainen, Antti
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951613894