eprintid: 1555643
rev_number: 23
eprint_status: archive
userid: 608
dir: disk0/01/55/56/43
datestamp: 2017-05-09 16:51:58
lastmod: 2021-11-15 01:45:23
status_changed: 2017-05-09 16:51:58
type: article
metadata_visibility: show
creators_name: Boedihardjo, H
creators_name: Ni, H
creators_name: Qian, Z
title: Uniqueness of signature for simple curves
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
keywords: Rough path theory; 
Uniqueness of signature problem; 
SLE curves
note: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two dimensional closed curve with finite p   variation, 1≤p<21≤p<2, are in fact moments of its winding number. This relation allows us to prove that the signature series of a class of simple non-smooth curves uniquely determine the curves. This implies that outside a Chordal SLEκSLEκ null set, where 0<κ≤40<κ≤4, the signature series of curves uniquely determine the curves. Our calculations also enable us to express the Fourier transform of the n-point functions of SLE curves in terms of the expected signature of SLE curves. Although the techniques used in this article are deterministic, the results provide a platform for studying SLE curves through the signatures of their sample paths.
date: 2014-09-15
date_type: published
official_url: https://doi.org/10.1016/j.jfa.2014.06.006
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
article_type_text: Article
verified: verified_manual
elements_id: 1159659
doi: 10.1016/j.jfa.2014.06.006
lyricists_name: Ni, Hao
lyricists_id: HNIXX56
actors_name: Flynn, Bernadette
actors_id: BFFLY94
actors_role: owner
full_text_status: public
publication: Journal of Functional Analysis
volume: 267
number: 6
pagerange: 1778-1806
issn: 0022-1236
citation:        Boedihardjo, H;    Ni, H;    Qian, Z;      (2014)    Uniqueness of signature for simple curves.                   Journal of Functional Analysis , 267  (6)   pp. 1778-1806.    10.1016/j.jfa.2014.06.006 <https://doi.org/10.1016/j.jfa.2014.06.006>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1555643/1/Boedihardjo_Uniqueness_of_signature_AAM.pdf