论文标题
小噪声随机反应扩散方程的系统满足了所有初始数据均匀的大偏差原理
Systems of small-noise stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over all initial data
论文作者
论文摘要
大偏差原则是罕见事件概率的指数衰减率的特征。 Cerrai and Rockner [13]证明，随机反应扩散方程的系统满足了一个大偏差原理，该原理在界限的初始数据集中均匀。 本文证明了随机反应系统的统一大偏差结果 - 与Cerrai和Rockner更一般的环境中的扩散方程式。此外，本文确定了两种常见情况，在这些情况下，大偏差原理在无限的初始数据集上是均匀的，从而使Freidlin-Wentzell退出时间和从无界集合的出口渐近造型的表征能够表征。
Large deviations principles characterize the exponential decay rates of the probabilities of rare events. Cerrai and Rockner [13] proved that systems of stochastic reaction-diffusion equations satisfy a large deviations principle that is uniform over bounded sets of initial data. This paper proves uniform large deviations results for a system of stochastic reaction--diffusion equations in a more general setting than Cerrai and Rockner. Furthermore, this paper identifies two common situations where the large deviations principle is uniform over unbounded sets of initial data, enabling the characterization of Freidlin-Wentzell exit time and exit shape asymptotics from unbounded sets.
