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...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
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 |
| Summary: | 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]. |
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