Rough path metrics on a Besov–Nikolskii-type scale
It is known, since the seminal work [T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana, 14 (1998)], that the solution map associated to a controlled differential equation is locally Lipschitz continuous in q-variation, resp., 1/q-H¨older-type metrics on the space of...
| Автори: | , |
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| Формат: | Journal article |
| Мова: | English |
| Опубліковано: |
American Mathematical Society
2017
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| _version_ | 1826282658642001920 |
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| author | Friz, P Prömel, D |
| author_facet | Friz, P Prömel, D |
| author_sort | Friz, P |
| collection | OXFORD |
| description | It is known, since the seminal work [T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana, 14 (1998)], that the solution map associated to a controlled differential equation is locally Lipschitz continuous in q-variation, resp., 1/q-H¨older-type metrics on the space of rough paths, for any regularity 1/q ∈ (0, 1]. We extend this to a new class of Besov–Nikolskii-type metrics, with arbitrary regularity 1/q ∈ (0, 1] and integrability p ∈ [q, ∞], where the case p ∈ {q,∞} corresponds to the known cases. Interestingly, the result is obtained as a consequence of known q-variation rough path estimates. |
| first_indexed | 2024-03-07T00:47:10Z |
| format | Journal article |
| id | oxford-uuid:85176163-c1b3-498c-a7fe-1dac15a59ddc |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:47:10Z |
| publishDate | 2017 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | oxford-uuid:85176163-c1b3-498c-a7fe-1dac15a59ddc2022-03-26T21:55:06ZRough path metrics on a Besov–Nikolskii-type scaleJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:85176163-c1b3-498c-a7fe-1dac15a59ddcEnglishSymplectic Elements at OxfordAmerican Mathematical Society2017Friz, PPrömel, DIt is known, since the seminal work [T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana, 14 (1998)], that the solution map associated to a controlled differential equation is locally Lipschitz continuous in q-variation, resp., 1/q-H¨older-type metrics on the space of rough paths, for any regularity 1/q ∈ (0, 1]. We extend this to a new class of Besov–Nikolskii-type metrics, with arbitrary regularity 1/q ∈ (0, 1] and integrability p ∈ [q, ∞], where the case p ∈ {q,∞} corresponds to the known cases. Interestingly, the result is obtained as a consequence of known q-variation rough path estimates. |
| spellingShingle | Friz, P Prömel, D Rough path metrics on a Besov–Nikolskii-type scale |
| title | Rough path metrics on a Besov–Nikolskii-type scale |
| title_full | Rough path metrics on a Besov–Nikolskii-type scale |
| title_fullStr | Rough path metrics on a Besov–Nikolskii-type scale |
| title_full_unstemmed | Rough path metrics on a Besov–Nikolskii-type scale |
| title_short | Rough path metrics on a Besov–Nikolskii-type scale |
| title_sort | rough path metrics on a besov nikolskii type scale |
| work_keys_str_mv | AT frizp roughpathmetricsonabesovnikolskiitypescale AT promeld roughpathmetricsonabesovnikolskiitypescale |