Open Access
Translator Disclaimer
November 2016 Characteristic functions of measures on geometric rough paths
Ilya Chevyrev, Terry Lyons
Ann. Probab. 44(6): 4049-4082 (November 2016). DOI: 10.1214/15-AOP1068


We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially solving the analogue of the moment problem. We furthermore study analyticity properties of the characteristic function and prove a method of moments for weak convergence of random variables. We apply our results to signature arising from Lévy, Gaussian and Markovian rough paths.


Download Citation

Ilya Chevyrev. Terry Lyons. "Characteristic functions of measures on geometric rough paths." Ann. Probab. 44 (6) 4049 - 4082, November 2016.


Received: 1 November 2014; Revised: 1 October 2015; Published: November 2016
First available in Project Euclid: 14 November 2016

zbMATH: 06674845
MathSciNet: MR3572331
Digital Object Identifier: 10.1214/15-AOP1068

Primary: 60B11
Secondary: 43A05

Keywords: accumulated local variation , Expected signature , Rough paths

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 6 • November 2016
Back to Top