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Uniqueness of signature for simple curves
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Boedihardjo, Horatio, Ni, Hao and Qian, Zhongmin (2014) Uniqueness of signature for simple curves. Journal of Functional Analysis, 267 (6). pp. 1778-1806. doi:10.1016/j.jfa.2014.06.006 ISSN 0022-1236.
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Official URL: http://dx.doi.org/10.1016/j.jfa.2014.06.006
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, , 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 null set, where , 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.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
| Library of Congress Subject Headings (LCSH): | Curves, Algebraic, Statistical physics, Probabilities, Functions of complex variables | ||||||
| Journal or Publication Title: | Journal of Functional Analysis | ||||||
| Publisher: | Academic Press | ||||||
| ISSN: | 0022-1236 | ||||||
| Official Date: | September 2014 | ||||||
| Dates: |
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| Volume: | 267 | ||||||
| Number: | 6 | ||||||
| Page Range: | pp. 1778-1806 | ||||||
| DOI: | 10.1016/j.jfa.2014.06.006 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Reuse Statement (publisher, data, author rights): | © 2014, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/. | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Date of first compliant deposit: | 22 July 2020 | ||||||
| Date of first compliant Open Access: | 22 July 2020 | ||||||
| RIOXX Funder/Project Grant: |
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