ROUGH PATHS AND HOPF ALGEBRAS

被引：0

作者：

Manchon, Dominique ^{[1
]}

机构：

[1] Univ Clermont Auvergne, CNRS, Clermont Ferrand, France

来源：

JOURNAL OF COMPUTATIONAL DYNAMICS | 2025年 / 12卷 / 01期

关键词：

Hopf algebras; rough paths; multi-indices; trees; pre-Lie algebras; post-Lie algebras; DIFFERENTIAL-EQUATIONS; RENORMALIZATION; SUBSTITUTION; INTEGRALS; THEOREM; TREES;

D O I：

10.3934/jcd.2024032

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Any commutative connected graded Hopf algebra gives rise to a specific notion of rough path. This article provides a review of the different Hopf algebras, providing the various kinds of rough paths which have appeared in recent literature: geometric and quasi-geometric rough paths, branched and planarly branched rough paths, and multi-index rough paths. Relations between all these variants are also described.

引用

页码：160 / 177

页数：18

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