TY  - JOUR
A1  - Bellingeri, Carlo
A1  - Friz, Peter
A1  - Paycha, Sylvie
A1  - Preiß, Rosa Lili Dora
T1  - Smooth rough paths, their geometry and algebraic renormalization
JF  - Vietnam journal of mathematics
N2  - We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the key to a purely algebraic form of Lyons' extension theorem, the renormalization of rough paths following up on [Bruned et al.: A rough path perspective on renormalization, J. Funct. Anal. 277(11), 2019], as well as a related notion of "sum of rough paths". We first develop our ideas in a geometric rough path setting, as this best resonates with recent works on signature varieties, as well as with the renormalization of geometric rough paths. We then explore extensions to the quasi-geometric and the more general Hopf algebraic setting.
KW  - Signatures
KW  - Rough paths
KW  - Cartan's development
KW  - Renormalization
Y1  - 2022
U6  - https://doi.org/10.1007/s10013-022-00570-7
SN  - 2305-221X
SN  - 2305-2228
VL  - 50
IS  - 3
SP  - 719
EP  - 761
PB  - Springer
CY  - Singapore
ER  -