Viscous Shock Solutions to the Stochastic Burgers Equation

We define a notion of viscous shock solution the stochastic Burgers equation that connects "top" and "bottom" spatially stationary solutions same equation. Such shocks generally travel in space, but we show they admit time-invariant measures when viewed their own reference frames. Under such measure, is deterministic function bottom top location. However, measure must be tilted to account for change frame. also convergence result these from initially connecting two constants, as time goes infinity.