  This paper deals with the combined incompressible quasineutral limit of the
weak martingale solution of the compressible Navier-Stokes-Poisson system
perturbed by a stochastic forcing term in the whole space. In the framework of
ill-prepared initial data, we show the convergence in law to a weak martingale
solution of a stochastic incompressible Navier-Stokes system. The result holds
true for any arbitrary nonlinear forcing term with suitable growth. The proof
is based on the analysis of acoustic waves but since we are dealing with a
stochastic partial differential equation, the existing deterministic tools for
treating this second-order equation breakdown. Although this might seem as a
minor modification, to handle the acoustic waves in the stochastic compressible
Navier-Stokes system, we produce suitable dispersive estimate for first-order
system of equations, which are an added value to the existing theory. As a
by-product of this dispersive estimate analysis, we are also able to prove a
convergence result in the case of the zero-electron-mass limit for a stochastic
fluid dynamical plasma model.
