A Freidlin–Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and the fast component is a stochastic reaction-diffusion equation. Our approach is via the weak convergence criterion developed in [A. Budhiraja and P. Dupuis, A variational representation for positive functionals of infinite dimensional Brownian motion, Probab. Math. Statist. 20 (2000) 39–61].

中文翻译：

---

两时间尺度随机汉堡方程的大偏差

建立了Freidlin-Wentzell型大偏差原理，用于具有慢速和快速时间尺度的随机偏微分方程，其中慢分量是噪声小的一维随机Burgers方程，快速分量是随机反应-扩散方程。我们的方法是通过 [A. Budhiraja 和 P. Dupuis，无限维布朗运动的正泛函的变分表示，概率。数学。统计学家。 20(2000) 39-61]。