The strong Feller property of the open KPZ equation
Alisa Knizel, Konstantin Matetski
TL;DR
This paper proves the strong Feller property for the semigroup of the open KPZ equation with Neumann boundary conditions and establishes the uniqueness of the stationary measure under certain parameter conditions.
Contribution
It demonstrates the strong Feller property for the open KPZ equation's semigroup and confirms the uniqueness of the stationary measure for specific boundary parameters.
Findings
Strong Feller property established for the open KPZ semigroup.
Uniqueness of stationary measure proven for certain boundary parameters.
Results support conjecture for all boundary parameter values.
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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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Stochastic processes and financial applications · Stochastic processes and statistical mechanics