Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations
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Sheffield_Absolute Continuity (arxiv).pdf
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Author(s)
Nahmod, Andrea
Rey-Bellet, Luc
Sheffield, Scott Roger
Staffilani, Gigliola
Date Issued
January 2011
Journal
Mathematical Research Letters
Publisher
International Press
Citation
Nahmod, Andrea R. et al."Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations." Mathematical Research Letters, 18.5 (2011): 875–887.
Version
Author's final manuscript
Abstract
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].
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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http://www.intlpress.com/_newsite/site/pub/pages/journals/items/mrl/content/vols/0018/0005/00020617/index.php
