Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Peter Friz (TU Berlin)
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.
(Joint works with Yvain Bruned, Ilya Chevyrev and Rosa Preiss).