论文标题
扩散的大偏差：Donsker-Varadhan Meet Freidlin-Wentzell
Large deviations for diffusions: Donsker-Varadhan meet Freidlin-Wentzell
论文作者
论文摘要
我们考虑$ \ Mathbb r^n $上的扩散过程，并在关节窗口差异和噪声消失的关节限制下证明了经验过程的大偏差原理。相应的速率函数由每单位时间的弗里德林 - 韦兹尔功能的期望给出。作为此结果的应用，我们获得了在小噪声和较大的时间限制中可观察到的Gallavotti-Cohen的速率函数的变异表示。
We consider a diffusion process on $\mathbb R^n$ and prove a large deviation principle for the empirical process in the joint limit in which the time window diverges and the noise vanishes. The corresponding rate function is given by the expectation of the Freidlin-Wentzell functional per unit of time. As an application of this result, we obtain a variational representation of the rate function for the Gallavotti-Cohen observable in the small noise and large time limits.
