Absolute continuity of Brownian bridges under certain gauge transformations
Analysis of PDEs
2011-03-25 v1 Classical Analysis and ODEs
Probability
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].
Keywords
Cite
@article{arxiv.1103.4822,
title = {Absolute continuity of Brownian bridges under certain gauge transformations},
author = {Andrea R. Nahmod and Luc Rey-Bellet and Scott Sheffield and Gigliola Staffilani},
journal= {arXiv preprint arXiv:1103.4822},
year = {2011}
}
Comments
12 pages. Submitted