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arXiv · 2211.04466

The strong Feller property of the open KPZ equation

Alisa Knizel·Konstantin Matetski
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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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Alisa Knizel, Konstantin Matetski. 2022-11-08. The strong Feller property of the open KPZ equation. https://arxiv.org/abs/2211.04466

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