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arXiv · 1605.02624

Paracontrolled calculus and Funaki-Quastel approximation for the KPZ equation

Masato Hoshino
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Abstract

In this paper, we consider the approximating KPZ equation introduced by Funaki and Quastel [2], which is suitable for studying invariant measures. They showed that the stationary solution of the approximating equation converges to the Cole-Hopf solution of the KPZ equation with extra term $(1/24)t$. On the other hand, Gubinelli and Perkowski [5] gave a pathwise meaning to the KPZ equation as an application of the paracontrolled calculus. We show that Funaki and Quastel's result is extended to nonstationary solutions by using the paracontrolled calculus.

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Masato Hoshino. 2017-02-26. Paracontrolled calculus and Funaki-Quastel approximation for the KPZ equation. https://arxiv.org/abs/1605.02624

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