×

zbMATH — the first resource for mathematics

Characteristic functions of measures on geometric rough paths. (English) Zbl 1393.60008
Summary: 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.

MSC:
60B11 Probability theory on linear topological spaces
43A05 Measures on groups and semigroups, etc.
PDF BibTeX XML Cite
Full Text: DOI arXiv