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.

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Cite This Study

Gu et al. (Thu,) studied this question.

synapsesocial.com/papers/68e02f3cf0e39f13e7fa25bd https://doi.org/https://doi.org/10.1090/tran/9542

Also Consider

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1Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States1965 · 4,118 citations
2On the replica approach to random directed polymers in two dimensions1990 · 93 citations
3An introduction to stochastic partial differential equations2006 · 2,352 citations
4KPZ equation, its renormalization and invariant measures2015 · 57 citations

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