Characteristic functions of measures on geometric rough paths
arXiv:1307.3580 · doi:10.1214/15-AOP1068
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.
29 pages, published version, updated refs