Ramification of rough paths
M. Gubinelli
TL;DR
This paper develops a non-geometric theory of rough paths by embedding iterated integrals into a larger algebraic structure involving decorated rooted trees and the D"urr-Connes-Kreimer coproduct, extending Chen's multiplicative property.
Contribution
It introduces a novel algebraic framework for rough paths using decorated rooted trees and coproducts, broadening the theoretical foundation beyond geometric rough paths.
Findings
Embedding iterated integrals in a tree-based algebraic structure
Extension of Chen's multiplicative property via coproducts
Establishment of a non-geometric rough path theory
Abstract
The stack of iterated integrals of a path is embedded in a larger algebraic structure where iterated integrals are indexed by decorated rooted trees and where an extended Chen's multiplicative property involves the D\"urr-Connes-Kreimer coproduct on rooted trees. This turns out to be the natural setting for a non-geometric theory of rough paths.
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Taxonomy
Topicsadvanced mathematical theories · Advanced Topics in Algebra · Advanced Algebra and Geometry