JournalsaihpcVol. 38, No. 4pp. 1217–1253

Homogenization of a stochastically forced Hamilton-Jacobi equation

  • Benjamin Seeger

    Université Paris-Dauphine & Collège de France, Place du Maréchal de Lattre de Tassigny, 75016 Paris, France
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Abstract

We study the homogenization of a Hamilton-Jacobi equation forced by rapidly oscillating noise that is colored in space and white in time. It is shown that the homogenized equation is deterministic, and, in general, the noise has an enhancement effect, for which we provide a quantitative estimate. As an application, we perform a noise sensitivity analysis for Hamilton-Jacobi equations forced by a noise term with small amplitude, and identify the scaling at which the macroscopic enhancement effect is felt. The results depend on new, probabilistic estimates for the large scale Hölder regularity of the solutions, which are of independent interest.

Cite this article

Benjamin Seeger, Homogenization of a stochastically forced Hamilton-Jacobi equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 4, pp. 1217–1253

DOI 10.1016/J.ANIHPC.2020.11.001