The Annals of Probability

Characteristic functions of measures on geometric rough paths

Ilya Chevyrev and Terry Lyons

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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.

Article information

Ann. Probab., Volume 44, Number 6 (2016), 4049-4082.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60B11: Probability theory on linear topological spaces [See also 28C20]
Secondary: 43A05: Measures on groups and semigroups, etc.

Rough paths expected signature accumulated local variation


Chevyrev, Ilya; Lyons, Terry. Characteristic functions of measures on geometric rough paths. Ann. Probab. 44 (2016), no. 6, 4049--4082. doi:10.1214/15-AOP1068.

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