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arXiv · 1307.3580

Characteristic functions of measures on geometric rough paths

Ilya Chevyrev·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.

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Ilya Chevyrev, Terry Lyons. 2017-05-18. Characteristic functions of measures on geometric rough paths. https://doi.org/10.1214/15-aop1068

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