October 3, 2025Transactions of the American Mathematical Society

Integration by parts and invariant measure for KPZ

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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.

Implication

Direct proof establishes drifted Brownian motions as invariant measures for the KPZ equation, highlighting mathematical relationships.

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. (2025) studied this question.

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

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Implication

Direct proof establishes drifted Brownian motions as invariant measures for the KPZ equation, highlighting mathematical relationships.

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.

Integration by parts and invariant measure for KPZ

Key Points

Implication

Abstract

Discussion

Cite This Study

Integration by parts and invariant measure for KPZ

Key Points

Implication

Abstract

Discussion

Cite This Study

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