## Electronic Communications in Probability

### Signature inversion for monotone paths

#### 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.

#### Article information

Source
Electron. Commun. Probab., Volume 22 (2017), paper no. 42, 11 pp.

Dates
Accepted: 23 June 2017
First available in Project Euclid: 15 August 2017

https://projecteuclid.org/euclid.ecp/1502762748

Digital Object Identifier
doi:10.1214/17-ECP70

Mathematical Reviews number (MathSciNet)
MR3693768

Zentralblatt MATH identifier
1378.60056

Subjects
Primary: 60

Keywords
signature inversion monotone paths

#### Citation

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

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