论文标题
小型制度中莱维扩散的巨大偏差
Large Deviations for Lévy Diffusions in small regime
论文作者
论文摘要
本文涉及较大的偏差制度以及Kramers问题的较大偏差解决方案，该问题是由小强度$ \ VAREPSILON> 0 $扰动的两次刻度随机系统驱动的，并以强度$ \ frac $ \ frac {1} {1} {\ varepsilon} $加速跳跃。我们使用弱收敛方法对大型偏差理论建立了多尺度系统慢速过程中的弗里德林 - 温泽尔估计。我们证明的核心是将大偏差原理减少到建立辅助控制过程的随机平均原理。结果，我们从一个有限的域中解决了第一个退出时间/退出基因座问题，该域中包含在小噪声限制中为缓慢过程的平均动力学稳定状态。
This article concerns the large deviations regime and the consequent solution of the Kramers problem for a two-time scale stochastic system driven by a common jump noise signal perturbed in small intensity $\varepsilon>0$ and with accelerated jumps by intensity $\frac{1}{\varepsilon}$. We establish Freidlin-Wentzell estimates for the slow process of the multiscale system in the small noise limit $\varepsilon \rightarrow 0$ using the weak convergence approach to large deviations theory. The core of our proof is the reduction of the large deviations principle to the establishment of a stochastic averaging principle for auxiliary controlled processes. As consequence we solve the first exit time/ exit locus problem from a bounded domain containing the stable state of the averaged dynamics for the family of the slow processes in the small noise limit.
