Characteristic functions of measures on geometric rough paths

Ilya Chevyrev, Terry Lyons

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)4049-4082
Number of pages29
JournalAnnals of Probability
Issue number6
Early online date14 Nov 2016
Publication statusPublished - 31 Dec 2016


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