Varieties of Signature Tensors
Probability
2019-12-04 v3 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1804.08325,
title = {Varieties of Signature Tensors},
author = {Carlos Améndola and Peter Friz and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1804.08325},
year = {2019}
}
Comments
52 pages, 1 figure, 6 tables; to appear in Forum of Mathematics, Sigma