Contents Online
Mathematical Research Letters
Volume 18 (2011)
Number 5
Absolute Continuity of Brownian Bridges Under Certain Gauge Transformations
Pages: 875 – 887
DOI: https://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}.
Published 28 October 2011