  In this paper, we study a nonlinear fluid-structure interaction problem
driven by a multiplicative, white-in-time noise. The problem consists of the
Navier-Stokes equations describing the flow of an incompressible, viscous fluid
in a 2D cylinder interacting with an elastic wall whose elastodynamics is
described by membrane equations. The stochastic force is applied both to the
fluid equations as a volumetric body force, and to the structure as an external
forcing to the deformable fluid boundary. The fluid and the structure are
nonlinearly coupled via the kinematic and dynamic conditions assumed at the
moving interface, which is a random variable not known a priori. In particular,
we consider the case where the structure is allowed to have non-zero
longitudinal displacement.
