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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2016
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/1603.00662 |
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| _version_ | 1866914967184211968 |
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| author | Boedihardjo, Horatio Geng, Xi Liu, Xuan Qian, Zhongmin |
| author_facet | Boedihardjo, Horatio Geng, Xi Liu, Xuan Qian, Zhongmin |
| contents | 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-self-intersecting. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1603_00662 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | A Quasi-sure Non-degeneracy Property for the Brownian Rough Path Boedihardjo, Horatio Geng, Xi Liu, Xuan Qian, Zhongmin Probability 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-self-intersecting. 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. |
| title | A Quasi-sure Non-degeneracy Property for the Brownian Rough Path |
| topic | Probability |
| url | https://arxiv.org/abs/1603.00662 |