  We consider a stochastic perturbation of the phase field alpha-Navier-Stokes
model with vesicle-fluid interaction. It consists in a system of nonlinear
evolution partial differential equations modeling the fluid-structure
interaction associated to the dynamics of an elastic vesicle immersed in a
moving incompressible viscous fluid. This system of equations couples a
phase-field equation -- for the interface between the fluid and the vesicle --
to the alpha-Navier-Stokes equation -- for the viscous fluid -- with an extra
nonlinear interaction term, namely the bending energy.
  The stochastic perturbation is an additive space-time noise of trace class on
each equation of the system. We prove the existence and uniqueness of solution
in classical spaces of $L^{2}$ functions with estimates of non-linear terms and
bending energy. It is based on a priori estimate about the regularity of
solutions of finite dimensional systems, and tightness of the approximated
solution.
