Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 22 (2017), paper no. 42, 11 pp.
Signature inversion for monotone paths
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.
Electron. Commun. Probab., Volume 22 (2017), paper no. 42, 11 pp.
Received: 8 February 2017
Accepted: 23 June 2017
First available in Project Euclid: 15 August 2017
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Chang, Jiawei; Duffield, Nick; Ni, Hao; Xu, Weijun. Signature inversion for monotone paths. Electron. Commun. Probab. 22 (2017), paper no. 42, 11 pp. doi:10.1214/17-ECP70. https://projecteuclid.org/euclid.ecp/1502762748