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