Partial sum process of orthogonal series as rough process
<p>In this thesis, we investigate the pathwise regularity of partial sum process of general orthogonal series, and prove that the partial sum process is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and...
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| Formaat: | Thesis |
| Taal: | English |
| Gepubliceerd in: |
2012
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| _version_ | 1826305032691122176 |
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| author | Yang, D |
| author2 | Lyons, T |
| author_facet | Lyons, T Yang, D |
| author_sort | Yang, D |
| collection | OXFORD |
| description | <p>In this thesis, we investigate the pathwise regularity of partial sum process of general orthogonal series, and prove that the partial sum process is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and an equivalent condition on the limit function is identified.</p> |
| first_indexed | 2024-03-07T06:26:43Z |
| format | Thesis |
| id | oxford-uuid:f48d69b9-29ba-420b-a6b5-55deba847b15 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T06:26:43Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:f48d69b9-29ba-420b-a6b5-55deba847b152022-03-27T12:20:40ZPartial sum process of orthogonal series as rough processThesishttp://purl.org/coar/resource_type/c_db06uuid:f48d69b9-29ba-420b-a6b5-55deba847b15Functional analysis (mathematics)EnglishOxford University Research Archive - Valet2012Yang, DLyons, T<p>In this thesis, we investigate the pathwise regularity of partial sum process of general orthogonal series, and prove that the partial sum process is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and an equivalent condition on the limit function is identified.</p> |
| spellingShingle | Functional analysis (mathematics) Yang, D Partial sum process of orthogonal series as rough process |
| title | Partial sum process of orthogonal series as rough process |
| title_full | Partial sum process of orthogonal series as rough process |
| title_fullStr | Partial sum process of orthogonal series as rough process |
| title_full_unstemmed | Partial sum process of orthogonal series as rough process |
| title_short | Partial sum process of orthogonal series as rough process |
| title_sort | partial sum process of orthogonal series as rough process |
| topic | Functional analysis (mathematics) |
| work_keys_str_mv | AT yangd partialsumprocessoforthogonalseriesasroughprocess |