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.
Original language | English |
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Pages (from-to) | 4049-4082 |
Number of pages | 29 |
Journal | Annals of Probability |
Volume | 44 |
Issue number | 6 |
Early online date | 14 Nov 2016 |
DOIs | |
Publication status | Published - 31 Dec 2016 |
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Ilya Chevyrev
- School of Mathematics - Reader in Probability and Stochastic Analysis
Person: Academic: Research Active (Teaching)