A Rough Path Perspective on Renormalization

Author: 

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

Publication Date: 

31 July 2019

Journal: 

Journal of Functional Analysis

Last Updated: 

2019-10-18T11:16:52.717+01:00

abstract: 

We develop the algebraic theory of rough path translation. Particular attention is given to the case of branched rough paths, whose underlying algebraic structure (Connes-Kreimer, Grossman-Larson) makes it a useful model case of a regularity structure in the sense of Hairer. Pre-Lie structures are seen to play a fundamental rule which allow a direct understanding of the translated (i.e. renormalized) equation under consideration. This construction is also novel with regard to the algebraic renormalization theory for regularity structures due to Bruned--Hairer--Zambotti (2016), the links with which are discussed in detail.

Symplectic id: 

991806

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article