Geodesic
VARIETIES OF SIGNATURE TENSORS
Forum of Mathematics, Sigma, Tome 7 (2019)

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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 examined here 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. 
@article{10_1017_fms_2019_3,
     author = {CARLOS AM\'ENDOLA and PETER FRIZ and BERND STURMFELS},
     title = {VARIETIES {OF} {SIGNATURE} {TENSORS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {7},
     year = {2019},
     doi = {10.1017/fms.2019.3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2019.3/}
}
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CARLOS AMÉNDOLA; PETER FRIZ; BERND STURMFELS. VARIETIES OF SIGNATURE TENSORS. Forum of Mathematics, Sigma, Tome 7 (2019). doi: 10.1017/fms.2019.3

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