A Rough Path Perspective on Renormalization


Bruned, Y
Chevyrev, I
Friz, P
Preiss, R

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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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Journal Article