The Signature of a Rough Path: Uniqueness
By H. Boedihardjo, X. Geng, Terry Lyons, Danyu Yang. 2014
146 citations recorded by the source corpus.
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.
Subfields: Computational Mechanics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/29770398386ebbafc232758dc325ab16d74ebaa0
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In Computational Mechanics
In Computational Theory and Mathematics
Citations in the corpus
- General Rough integration, Levy Rough paths and a Levy--Kintchine type formula (2012, background): “One could define G4(Rd)-valued Lévy rough paths, with pvariation regularity where p ∈ [4,5), an example of which is given by area-valued Brownian motion.”
- Joint calibration to SPX and VIX options with signature‐based models (2023, background): “The result is known in the rough paths literature (see for instance Boedihardjo et al. (2016)), but can also be proved directly in the simpler situation of a continuous semimartingale that contains time as strictly monotone component.”
- Characteristic functions of measures on geometric rough paths (2013, background): “Recall that every centred continuous Gaussian process in R with independent components and covariance matrix of finite 2D ρ-variation, ρ ∈ [1,2), admits a natural lift to a G p(R)-valued random variable X for any p > 2ρ ([15] Theorem 15.”