Stationary solutions to stochastic 3D Euler equations in Hölder space

We establish the existence of infinitely many global and stationary solutions in C(ℝ;C^ϑ) space for some ϑ>0 to the three dimensional Euler equations driven by an additive noise. The result is based on a new stochastic version of the convex integration method, incorporating the stochastic convex integration method developed in and pathwise estimates to derive uniform moment estimates independent of time.