Stationary Solutions to the Stochastic Burgers Equation on the Line

We consider invariant measures for the stochastic Burgers equation on \({\mathbb {R}}\), forced by derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth space. An measure indecomposable, or extremal, if it cannot be represented as convex combination other measures. show each \(a\in {\mathbb there unique indecomposable law spacetime-stationary solution with mean a, suitable function also solutions starting from spatially-decaying perturbations mean-a periodic functions converge to extremal space-time stationary goes infinity.