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# Mathematical Research Letters

## Volume 18 (2011)

### Number 5

### Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations

Pages: 875 – 887

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n5.a6

#### Authors

#### 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 Schrödinger equation obtained by Nahmod, *et al*, in \cite{NORBS}, and with respect to which they proved almost surely global well-posedness, coincides with the weighted Wiener measure constructed by Thomann and Tzvetkov \cite{TTzv}. Thus, in particular we prove the invariance of the measure constructed in \cite{TTzv}.