The Annals of Probability

Characteristic functions of measures on geometric rough paths

Ilya Chevyrev and Terry Lyons

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aop/1479114270

Digital Object Identifier
doi:10.1214/15-AOP1068

Mathematical Reviews number (MathSciNet)
MR3572331

Zentralblatt MATH identifier
06674845

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

Keywords
Rough paths expected signature accumulated local variation

Citation

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. https://projecteuclid.org/euclid.aop/1479114270


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