Characteristic functions of measures on geometric rough paths
Probability
2017-05-19 v6
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 L\'evy, Gaussian and Markovian rough paths.
Keywords
Cite
@article{arxiv.1307.3580,
title = {Characteristic functions of measures on geometric rough paths},
author = {Ilya Chevyrev and Terry Lyons},
journal= {arXiv preprint arXiv:1307.3580},
year = {2017}
}
Comments
29 pages, published version, updated refs