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A quasi-sure non-degeneracy property for the Brownian rough path
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Boedihardjo, Horatio, Geng, Xi, Liu, Xuan and Qian, Zhongmin (2019) A quasi-sure non-degeneracy property for the Brownian rough path. A quasi-sure non-degeneracy property for the Brownian rough path, 51 (1). pp. 1-21. doi:10.1007/s11118-018-9699-1
An open access version can be found in:
Official URL: http://doi.org/10.1007/s11118-018-9699-1
Abstract
In the present paper, we are going to show that outside a slim set in the sense of Malliavin (or quasi-surely), the signature path (which consists of iterated path integrals in every degree) of Brownian motion is non-selfintersecting. This property relates closely to a non-degeneracy property for the Brownian rough path arising naturally from the uniqueness of signature problem in rough path theory. As an important consequence we conclude that quasi-surely, the Brownian rough path does not have any tree-like pieces and every sample path of Brownian motion is uniquely determined by its signature up to reparametrization.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science > Mathematics | ||||||
| Journal or Publication Title: | A quasi-sure non-degeneracy property for the Brownian rough path | ||||||
| Publisher: | Springer | ||||||
| ISSN: | 0926-2601 | ||||||
| Official Date: | 7 May 2019 | ||||||
| Dates: |
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| Volume: | 51 | ||||||
| Number: | 1 | ||||||
| Page Range: | pp. 1-21 | ||||||
| DOI: | 10.1007/s11118-018-9699-1 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||
| Open Access Version: |
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