Integration by parts and invariant measure for KPZ
Yu Gu, Jeremy Quastel
TL;DR
This paper uses Stein's method and Gaussian integration by parts to directly prove that drifted Brownian motions serve as invariant measures for the KPZ equation, clarifying their relationship.
Contribution
It offers a new direct proof of the invariance of drifted Brownian motions for KPZ using Stein's method, enhancing understanding of the equation's invariant measures.
Findings
Drifted Brownian motions are invariant measures for KPZ.
Stein's method provides a new proof technique for invariance.
Gaussian integration by parts is key to the proof.
Abstract
Using Stein's method and a Gaussian integration by parts, we provide a direct proof of the known fact that drifted Brownian motions are invariant measures (modulo height) for the KPZ equation.
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Taxonomy
TopicsFunctional Equations Stability Results · Polynomial and algebraic computation · Holomorphic and Operator Theory