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- W2107841296 abstract "The signature of a $d$-dimensional Brownian motion is a sequence of iterated Stratonovich integrals along the Brownian paths, an object taking values in the tensor algebra over $mathbb{R}^{d}$. In this article, we derive the exact rate of convergence for the expected signatures of piecewise linear approximations to Brownian motion. The computation is based on the identification of the set of words whose coefficients are of the leading order, and the convergence is concentrated on this subset of words. Moreover, under the choice of $l^{1}$ tensor norm, we give the explicit value of the leading term constant." @default.
- W2107841296 created "2016-06-24" @default.
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- W2107841296 date "2015-01-01" @default.
- W2107841296 modified "2023-09-24" @default.
- W2107841296 title "Concentration and exact convergence rates for expected Brownian signatures" @default.
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- W2107841296 doi "https://doi.org/10.1214/ecp.v20-3636" @default.
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