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arXiv · 1701.01152

A Rough Path Perspective on Renormalization

Yvain Bruned·Ilya Chevyrev·Peter K. Friz·Rosa Preiss
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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.

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Yvain Bruned, Ilya Chevyrev, Peter K. Friz, Rosa Preiss. 2017-01-04. A Rough Path Perspective on Renormalization. https://doi.org/10.1016/j.jfa.2019.108283

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