Dynamics of stochastic Klein--Gordon--Schrödinger equations in unbounded domains

The long-time behavior in the sense of distributions for stochastic Klein-Gordon-Schrödinger equations in the whole space R n , 1 ≤ n ≤ 3, is studied.First the existence of one stationary measure from any moment-finite initial data in the spaceproved and then a global measure attractor is constructed in the space consisting of probability measures supported onBecause of the lack of compact embedding, some a priori estimates and a split of solutions play important roles in the approach.