Adding rough paths: no problem as long as they are smooth

Rosa Preiß (U of Potsdam)

Nov 08. 2021, 15:25 — 15:50

Joint with Carlo Bellingeri, Peter Friz and Sylvie Paycha

With thanks to Terry Lyons

It has become common folklore in rough path analysis that spaces of weakly geometric, quasi geometric or branched rough paths do not carry any meaningful notion of vector field structure, that their sum can in general only made sense of in terms of a non-unique Lyons-Victoir coupling. However, the situation drastically changes if one restricts to the at first sight seemingly paradox concept of smooth rough paths. We briefly present the Lie group theoretic aspect behind this surprising construction, show how it emerges from an 1998 statement of Lyons and explain how this sum is connected to the Bruned-Chevyrev-Friz-P. renormalization of rough paths applied to smooth rough paths.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation (Graduate School)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)