Characteristic functions of measures on geometric rough paths

Author: 

Chevyrev, I
Lyons, T

Publication Date: 

14 November 2016

Journal: 

Annals of Probability

Last Updated: 

2019-06-06T08:28:51.407+01:00

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 L\'evy, Gaussian and Markovian rough paths.

Symplectic id: 

502234

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article