Pith. sign in

REVIEW 1 cited by

The Signature of a Rough Path: Uniqueness

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1406.7871 v3 pith:MNZUFX37 submitted 2014-06-30 math.CA

classification math.CA
keywords pathpathssignaturereducedroughspacetree-likeapproach
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend Hambly-Lyons' result and their notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space. At the heart of our approach is a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Rough kernel hedging

    math.FA 2025-01 conditional novelty 6.0 of 10

    A signature-kernel and operator-valued-kernel framework for hedging is proved to have a unique global minimizer with an explicit formula, and it approximates the delta hedge on a GBM example.

Pith tools