Integration by parts and invariant measure for KPZ | Synapse
October 3, 2025
Integration by parts and invariant measure for KPZ
Key Points
Drifted Brownian motions serve as invariant measures for the KPZ equation.
Using Stein’s method and Gaussian integration, a direct proof of this relationship is provided.
This proof enhances understanding of invariant measures and their applications in stochastic processes.
The results underline the significance of integration techniques in studying the KPZ equation.
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.