Characteristic functions of measures on geometric rough paths

Author: 

Chevyrev, I
Lyons, T

Publication Date: 

14 November 2016

Journal: 

Annals of Probability

Last Updated: 

2020-11-06T21:25:13.393+00:00

Issue: 

6

Volume: 

44

DOI: 

10.1214/15-AOP1068

page: 

4049-4082

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.

Symplectic id: 

502234

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article