SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 4, Page 2469-2499, January 2020.
In this paper we establish the meta-stability of traveling waves for a class of reaction-diffusion equations forced by a multiplicative noise term. In particular, we show that the phase-tracking technique developed in [C. H. S. Hamster and H. J. Hupkes, SIAM J. Appl. Dyn. Syst., 18, pp. 205--278; Phys. D, 401, 132233] can be maintained over timescales that are exponentially long with respect to the noise intensity. This is achieved by combining the generic chaining principle with a mild version of the Burkholder--Davis--Gundy inequality to establish logarithmic supremum bounds for stochastic convolutions in the critical regularity regime.

中文翻译：

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随机反应扩散方程中行波在指数长尺度上的稳定性

SIAM应用动力系统杂志，第19卷，第4期，第2469-2499页，2020
年1月。在本文中，我们针对由乘性噪声项强迫产生的一类反应扩散方程，建立了行波的亚稳定性。尤其是，我们证明了在[CHS Hamster和HJ Hupkes，SIAM J. Appl。达因 Syst。，18，205--278页; 物理 D，401、132233]可以在相对于噪声强度呈指数增长的时标上保持。这是通过将泛型链原理与Burkholder-Davis-Gundy不等式的温和形式相结合来建立临界规则性制度中随机卷积的对数最高界而实现的。