ABSOLUTE CONTINUITY OF BROWNIAN BRIDGES UNDER CERTAIN GAUGE TRANSFORMATIONS

作者：Nahmod Andrea R^*; Rey Bellet Luc; Sheffield Scott; Staffilani Gigliola

来源：Mathematical Research Letters, 2011, 18(5): 875-887.

DOI：10.4310/mrl.2011.v18.n5.a6

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 Schrodinger equation obtained by Nahmod, et al. 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].

• 出版日期2011-9