Renormalised singular stochastic PDEs
Probability
2021-02-03 v2 Analysis of PDEs
Rings and Algebras
Abstract
Extended decorations on naturally decorated trees were introduced in the work of Bruned, Hairer and Zambotti on algebraic renormalization of regularity structures to provide a convenient framework for the renormalization of systems of singular stochastic PDEs within that setting. This non-dynamical feature of the trees complicated the analysis of the dynamical counterpart of the renormalization process. We provide a new proof of the renormalized system by-passing the use of extended decorations and working for a large class of renormalization maps, with the BPHZ renormalization as a special case. The proof reveals important algebraic properties connected to preparation maps.
Cite
@article{arxiv.2101.11949,
title = {Renormalised singular stochastic PDEs},
author = {Ismael Bailleul and Yvain Bruned},
journal= {arXiv preprint arXiv:2101.11949},
year = {2021}
}