Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations
We prove absolute continuity of Gaussian measures associated to complex Brownian bridges under certain gauge transformations. As an application we prove that the invariant measure for the periodic derivative nonlinear Schr ¨odinger equation obtained by Nahmod, Oh, Rey-Bellet and Staffilani in [20...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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International Press
2012
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| Online Access: | http://hdl.handle.net/1721.1/71841 https://orcid.org/0000-0002-5951-4933 https://orcid.org/0000-0002-8220-4466 |
| _version_ | 1826203165038477312 |
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| author | Nahmod, Andrea Rey-Bellet, Luc Sheffield, Scott Roger Staffilani, Gigliola |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Nahmod, Andrea Rey-Bellet, Luc Sheffield, Scott Roger Staffilani, Gigliola |
| author_sort | Nahmod, Andrea |
| collection | MIT |
| description | We prove absolute continuity of Gaussian measures associated to complex
Brownian bridges under certain gauge transformations. As an application we prove that
the invariant measure for the periodic derivative nonlinear Schr ¨odinger equation obtained
by Nahmod, Oh, Rey-Bellet and Staffilani in [20], and with respect to which they proved
almost surely global well-posedness, coincides with the weighted Wiener measure constructed
by Thomann and Tzvetkov [24]. Thus, in particular we prove the invariance of the
measure constructed in [24]. |
| first_indexed | 2024-09-23T12:32:21Z |
| format | Article |
| id | mit-1721.1/71841 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T12:32:21Z |
| publishDate | 2012 |
| publisher | International Press |
| record_format | dspace |
| spelling | mit-1721.1/718412022-10-01T09:39:11Z Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations Nahmod, Andrea Rey-Bellet, Luc Sheffield, Scott Roger Staffilani, Gigliola Massachusetts Institute of Technology. Department of Mathematics Sheffield, Scott Roger Sheffield, Scott Roger Staffilani, Gigliola We prove absolute continuity of Gaussian measures associated to complex Brownian bridges under certain gauge transformations. As an application we prove that the invariant measure for the periodic derivative nonlinear Schr ¨odinger equation obtained by Nahmod, Oh, Rey-Bellet and Staffilani in [20], and with respect to which they proved almost surely global well-posedness, coincides with the weighted Wiener measure constructed by Thomann and Tzvetkov [24]. Thus, in particular we prove the invariance of the measure constructed in [24]. 2012-07-26T17:36:33Z 2012-07-26T17:36:33Z 2011-01 2011-03 Article http://purl.org/eprint/type/JournalArticle 1073-2780 1945-001X http://hdl.handle.net/1721.1/71841 Nahmod, Andrea R. et al."Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations." Mathematical Research Letters, 18.5 (2011): 875–887. https://orcid.org/0000-0002-5951-4933 https://orcid.org/0000-0002-8220-4466 en_US http://www.intlpress.com/_newsite/site/pub/pages/journals/items/mrl/content/vols/0018/0005/00020617/index.php Mathematical Research Letters Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf International Press arXiv |
| spellingShingle | Nahmod, Andrea Rey-Bellet, Luc Sheffield, Scott Roger Staffilani, Gigliola Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations |
| title | Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations |
| title_full | Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations |
| title_fullStr | Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations |
| title_full_unstemmed | Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations |
| title_short | Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations |
| title_sort | absolute continuity of brownian bridges under certain gauge transformations |
| url | http://hdl.handle.net/1721.1/71841 https://orcid.org/0000-0002-5951-4933 https://orcid.org/0000-0002-8220-4466 |
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