Ni, H;
Xu, W;
(2015)
Concentration and exact convergence rates for expected Brownian signatures.
Electronic Communications in Probability
, 20
(8)
10.1214/ECP.v20-3636.
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Abstract
The signature of a dd-dimensional Brownian motion is a sequence of iterated Stratonovich integrals along the Brownian paths, an object taking values in the tensor algebra over RdRd. 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 l1l1 tensor norm, we give the explicit value of the leading term constant.
| Type: | Article |
|---|---|
| Title: | Concentration and exact convergence rates for expected Brownian signatures |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1214/ECP.v20-3636 |
| Publisher version: | http://dx.doi.org/ 10.1214/ECP.v20-3636 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution 3.0 License (http://creativecommons.org/licenses/by/3.0/). |
| Keywords: | Expected signature; Brownian motion |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1516164 |
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