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A rough path perspective on renormalization

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https://arxiv.org/abs/1701.01152
Original languageEnglish
Article number108283
Number of pages60
JournalJournal of functional analysis
Volume277
Issue number11
Early online date31 Jul 2019
DOIs
Publication statusPublished - 1 Dec 2019

Abstract

We revisit (higher-order) translation operators on rough paths, in both the geometric and branched setting. As in Hairer's work on the renormalization of singular SPDEs we propose a purely algebraic view on the matter. Recent advances in the theory of regularity structures, especially the Hopf algebraic interplay of positive and negative renormalization of Bruned-Hairer-Zambotti (2016), are seen to have precise counterparts in the rough path context, even with a similar formalism (short of polynomial decorations and colourings). Renormalization is
then seen to correspond precisely to (higher-order) rough path translation.

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