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Signature inversion for monotone paths

Ni, H; Xu, W; Chang, J; Duffield, N; (2017) Signature inversion for monotone paths. Electronic Communications in Probability , 42 , Article 11. 10.1214/17-ECP70. Green open access

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Abstract

The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the signature. We show that these weights on lattice paths satisfy the large deviations principle. In particular, this implies that the probability of picking up a “wrong” path is exponentially small in N. The argument relies on a probabilistic interpretation of the signature for monotone paths.

Type: Article
Title: Signature inversion for monotone paths
Open access status: An open access version is available from UCL Discovery
DOI: 10.1214/17-ECP70
Publisher version: http://dx.doi.org/10.1214/17-ECP70
Language: English
Additional information: This is an Open Access article published under a Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).
Keywords: Signature, inversion, monotone paths
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/1569460
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