The uniqueness of signature problem in the non-Markov setting

H. Boedihardjo and X. Geng

Stochastic Processes and their Applications, 2015, vol. 125, issue 12, 4674-4701

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.

Keywords: Gaussian rough paths; Uniqueness of signature; The Malliavin calculus (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.07.012

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