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The uniqueness of signature problem in the non-Markov setting
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Boedihardjo, Horatio and Geng, Xi (2015) The uniqueness of signature problem in the non-Markov setting. Stochastic Processes and their Applications, 125 (12). pp. 4674-4701. doi:10.1016/j.spa.2015.07.012 ISSN 0304-4149.
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Official URL: https://www.sciencedirect.com/science/article/pii/...
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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||
Journal or Publication Title: | Stochastic Processes and their Applications | ||||||||
Publisher: | Elsevier | ||||||||
ISSN: | 0304-4149 | ||||||||
Official Date: | December 2015 | ||||||||
Dates: |
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Volume: | 125 | ||||||||
Number: | 12 | ||||||||
Page Range: | pp. 4674-4701 | ||||||||
DOI: | 10.1016/j.spa.2015.07.012 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
RIOXX Funder/Project Grant: |
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Open Access Version: |
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