Journal article
The uniqueness of signature problem in the non-Markov setting
H Boedihardjo, X Geng
Stochastic Processes and their Applications | ELSEVIER | Published : 2015
Abstract
We establish a general framework for a class of multidimensional stochastic processes over [0,1] under which with probability one, the signature (the collection of iterated path integrals in the sense of rough paths) is well-defined and determines the sample paths of the process up to reparametrization. In particular, by using the Malliavin calculus we show that our method applies to a class of Gaussian processes including fractional Brownian motion with Hurst parameter H>1/4, the Ornstein-Uhlenbeck process and the Brownian bridge.
Grants
Awarded by European Research Council
Funding Acknowledgements
The authors wish to thank Professor Zhongmin Qian for his valuable suggestions on this work, and the referees for their very careful reading and helpful comments on the present paper. The authors are supported by the ERC grant (Grant Agreement No. 291244 Esig).