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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

Abstract

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.

Citation

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Ilya Chevyrev. Terry Lyons. "Characteristic functions of measures on geometric rough paths." Ann. Probab. 44 (6) 4049 - 4082, November 2016. https://doi.org/10.1214/15-AOP1068

Information

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

Subjects:
Primary: 60B11
Secondary: 43A05

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 6 • November 2016
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