Limit theorems for signatures
Abstract
We obtain strong moment invariance principles for normalized multiple iterated sums and integrals of the form SN(ν)(t)=N−ν∕2∑0≤k12 relying on arguments borrowed from the rough paths theory. In the continuous time we work both under direct weak dependence assumptions and also within the suspension setup which is more appropriate for applications in dynamical systems. In Appendix we derive large deviations estimates for iterated sums and integrals.
Fields of Study & Subjects
Stochastic processes and financial applications
Insurance
Mortality
Demography
Risk Management
Publication details
- Journal / source
- Electronic Journal of Probability
- Publisher
- Institute of Mathematical Statistics
- Volume
- 31
- Issue
- none
- Pages
- 1-53
- Publication date
- 1 January 2026
- Language
- EN