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Absolute continuity of Brownian bridges under certain gauge transformations

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arxiv 1103.4822 v1 pith:OTKAHH2F submitted 2011-03-24 math.AP math.CAmath.PR

Andrea R. Nahmod , Luc Rey-Bellet , Scott Sheffield , Gigliola Staffilani This is my paper
classification math.APmath.CAmath.PR
keywords measureproveabsolutebridgesbrowniancertainconstructedcontinuity
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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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