  We prove the existence of martingale solutions to a stochastic
fluid-structure interaction problem involving a viscous, incompressible fluid
flow, modeled by the Navier-Stokes equations, through a deformable elastic tube
modeled by shell/membrane equations. The fluid and the structure are
nonlinearly coupled via the kinematic and dynamic coupling conditions at the
fluid-structure interface. This article considers the case where the structure
can have unrestricted displacement and explores the Navier-slip boundary
condition imposed at the fluid-structure interface, displacement of which is
not known a priori and is itself a part of the solution. The proof takes a
constructive approach based on a Lie splitting scheme. The geometric
nonlinearity stemming from the nonlinear coupling, the possibility of random
fluid domain degeneracy, the potential jumps in the tangential components of
the fluid and structure velocities at the moving interface and the low
regularity of the structure velocity require the development of new techniques
that lead to the existence of martingale solutions.
