论文标题
反射扩散的动力大偏差
Dynamical large deviations of reflected diffusions
论文作者
论文摘要
我们研究了具有完美反映界限的马尔可夫扩散的时间融合的巨大偏差。我们讨论如何通过施加零电流条件，导致诺伊曼或罗宾边界条件来修改动态大偏差的标准光谱方法，以解决此类界限，以及这些条件如何影响驱动过程，这描述了长期限制中大偏差的出现。结果用漂移的布朗运动和Ornstein-Uhlenbeck的过程进行了说明。讨论了其他类型的边界和应用程序。
We study the large deviations of time-integrated observables of Markov diffusions that have perfectly reflecting boundaries. We discuss how the standard spectral approach to dynamical large deviations must be modified to account for such boundaries by imposing zero-current conditions, leading to Neumann or Robin boundary conditions, and how these conditions affect the driven process, which describes how large deviations arise in the long-time limit. The results are illustrated with the drifted Brownian motion and the Ornstein-Uhlenbeck process reflected at the origin. Other types of boundaries and applications are discussed.
