The Uniqueness of Signature Problem in the Non-Markov Setting

Horatio Boedihardjo; Xi Geng

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arXiv · 1401.6165

The Uniqueness of Signature Problem in the Non-Markov Setting

Horatio Boedihardjo·Xi Geng

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Abstract

The goal of this paper is to simplify and strengthen the Le Jan-Qian approximation scheme of studying the uniqueness of signature problem to the non-Markov setting. 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.

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BibTeX RIS

Horatio Boedihardjo, Xi Geng. 2014-07-17. The Uniqueness of Signature Problem in the Non-Markov Setting. https://arxiv.org/abs/1401.6165

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