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The strong Feller property of the open KPZ equation (2211.04466v1)
Published 8 Nov 2022 in math.PR, math-ph, math.AP, and math.MP
Abstract: We prove that the semigroup generated by the open KPZ equation on a bounded spatial interval with Neumann boundary conditions parametrized by real parameters u and v enjoys the strong Feller property. From this we conclude that for u+v>0, min(u,v)>-1 the stationary measure constructed in Corwin and Knizel (arXiv:2103.12253) is the unique stationary measure for the equation. It is expected that the same conclusion holds for all values of u and v.
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