Stationary Solutions to the Stochastic Burgers Equation on the Line

@article{Dunlap2019StationaryST,
  title={Stationary Solutions to the Stochastic Burgers Equation on the Line},
  author={Alexander Dunlap and Cole Graham and Lenya Ryzhik},
  journal={arXiv: Probability},
  year={2019}
}
We consider invariant measures for the stochastic Burgers equation on $\mathbb{R}$, forced by the derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth in space. An invariant measure is indecomposable, or extremal, if it cannot be represented as a convex combination of other invariant measures. We show that for each $a\in\mathbb{R}$, there is a unique indecomposable law of a spacetime-stationary solution with mean $a$, in a suitable function space. We also show… 
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