کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4590060 1334930 2014 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Uniqueness of signature for simple curves
ترجمه فارسی عنوان
منحصر به فرد امضا برای منحنی های ساده
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 267, Issue 6, 15 September 2014, Pages 1778–1806
نویسندگان
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