Fine properties of fractional Brownian motions on Wiener space
We study several important fine properties for the family of fractional Brownian motions with Hurst parameter H under the p,r -capacity on classical Wiener space introduced by Malliavin. We regard fractional Brownian motions as Wiener functionals via the integral representation discovered by Decreus...
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| Formato: | Journal article |
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Elsevier
2018
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| _version_ | 1826256959246958592 |
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| author | Jiawei, L Qian, Z |
| author_facet | Jiawei, L Qian, Z |
| author_sort | Jiawei, L |
| collection | OXFORD |
| description | We study several important fine properties for the family of fractional Brownian motions with Hurst parameter H under the p,r -capacity on classical Wiener space introduced by Malliavin. We regard fractional Brownian motions as Wiener functionals via the integral representation discovered by Decreusefond and Üstünel, and show non-differentiability, modulus of continuity, law of the iterated logarithm (LIL) and self-avoiding properties of fractional Brownian motion sample paths using Malliavin calculus as well as the tools developed in the previous work by Fukushima, Takeda and etc. for Brownian motion case. |
| first_indexed | 2024-03-06T18:10:32Z |
| format | Journal article |
| id | oxford-uuid:02ddd9aa-88d5-4442-a66c-e2e1ace20c27 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:10:32Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:02ddd9aa-88d5-4442-a66c-e2e1ace20c272022-03-26T08:43:06ZFine properties of fractional Brownian motions on Wiener spaceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:02ddd9aa-88d5-4442-a66c-e2e1ace20c27Symplectic Elements at OxfordElsevier2018Jiawei, LQian, ZWe study several important fine properties for the family of fractional Brownian motions with Hurst parameter H under the p,r -capacity on classical Wiener space introduced by Malliavin. We regard fractional Brownian motions as Wiener functionals via the integral representation discovered by Decreusefond and Üstünel, and show non-differentiability, modulus of continuity, law of the iterated logarithm (LIL) and self-avoiding properties of fractional Brownian motion sample paths using Malliavin calculus as well as the tools developed in the previous work by Fukushima, Takeda and etc. for Brownian motion case. |
| spellingShingle | Jiawei, L Qian, Z Fine properties of fractional Brownian motions on Wiener space |
| title | Fine properties of fractional Brownian motions on Wiener space |
| title_full | Fine properties of fractional Brownian motions on Wiener space |
| title_fullStr | Fine properties of fractional Brownian motions on Wiener space |
| title_full_unstemmed | Fine properties of fractional Brownian motions on Wiener space |
| title_short | Fine properties of fractional Brownian motions on Wiener space |
| title_sort | fine properties of fractional brownian motions on wiener space |
| work_keys_str_mv | AT jiaweil finepropertiesoffractionalbrownianmotionsonwienerspace AT qianz finepropertiesoffractionalbrownianmotionsonwienerspace |