The uniqueness of signature problem in the non-Markov settingBoedihardjo, H. and Geng, X. (2015) The uniqueness of signature problem in the non-Markov setting. Stochastic Processes and their Applications, 125 (12). pp. 4674-4701. ISSN 0304-4149 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1016/j.spa.2015.07.012 Abstract/SummaryWe 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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