Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation

Abstract

We consider the cubic fourth order nonlinear Schrödinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces $H^s(\mathbb{T})$, $s > \frac34$, are quasi-invariant under the flow.

41 pages. To appear in Probab. Theory Related Fields