Note on the Signatures of Rough Paths in a Banach Space
Horatio Boedihardjo, Xi Geng, Terry Lyons, Danyu Yang
TL;DR
This paper extends known properties of weakly geometric rough paths from finite-dimensional spaces to infinite-dimensional Banach spaces, providing foundational proofs needed for advanced rough path analysis.
Contribution
It offers new proofs of properties of weakly geometric rough paths in Banach spaces, filling a gap in the infinite-dimensional theory.
Findings
Established key properties of rough paths in Banach spaces
Extended finite-dimensional rough path results to infinite dimensions
Provided rigorous proofs for use in subsequent research
Abstract
We prove some results, which are used in arXiv:1406.7871, about weakly geometric rough paths that are well-known in finite dimensions, but need proof in the infinite dimensional setting.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Limits and Structures in Graph Theory · Algebraic Geometry and Number Theory