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Mathematics > Probability

arXiv:1804.08325 (math)
[Submitted on 23 Apr 2018 (v1), last revised 15 Jan 2019 (this version, v3)]

Title:Varieties of Signature Tensors

Authors:Carlos Améndola, Peter Friz, Bernd Sturmfels
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Abstract:The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry. We introduce varieties of signature tensors for both deterministic paths and random paths. For the former, we focus on piecewise linear paths, on polynomial paths, and on varieties derived from free nilpotent Lie groups. For the latter, we focus on Brownian motion and its mixtures.
Comments: 52 pages, 1 figure, 6 tables; to appear in Forum of Mathematics, Sigma
Subjects: Probability (math.PR); Algebraic Geometry (math.AG)
MSC classes: 14Q15, 60H99
Cite as: arXiv:1804.08325 [math.PR]
  (or arXiv:1804.08325v3 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1804.08325
Journal reference: Forum of Mathematics, Sigma 7 (2019) e10
Related DOI: https://doi.org/10.1017/fms.2019.3

Submission history

From: Carlos Améndola [view email]
[v1] Mon, 23 Apr 2018 10:25:19 UTC (55 KB)
[v2] Fri, 12 Oct 2018 14:51:55 UTC (74 KB)
[v3] Tue, 15 Jan 2019 15:35:08 UTC (87 KB)
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