Integration of time-varying cocyclic one-forms against rough paths

2014/08/12 by Terry Lyons, Lyons, Terry J., Danyu Yang +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1408.2785

openalex publication_date 2014/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We embed the rough integration in a larger geometrical/algebraic framework of integrating one-forms against group-valued paths, and reduce the rough integral to an inhomogeneous analogue of the classical Young integral. We define dominated paths as integrals of one-forms, and demonstrate that they are stable under basic operations.

Citations

• An inequality of the Hölder type, connected with Stieltjes integration

Related

• The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations
• Controlling Rough Paths
• Controlled Rough Paths on Manifolds I
• Differential Equations driven by Π-rough paths
• Towards geometric integration of rough differential forms