平面流的噪声诱导稳定性II
Noise-Induced Stabilization of Planar Flows II
摘要：
我们继续本文第一部分中开始的工作，展示如何添加噪声来稳定一个不稳定的系统。该分析利用了接近最优的李雅普诺夫函数。在这个延续中，我们通过归纳过程去除了第一部分的主要限制假设，并建立了一个下界，表明我们的构造是径向尖锐的。我们还证明了一个版本的Peskir的\cite{Peskir_07}广义田中公式适用于修补在一起的李雅普诺夫函数。这大大简化了以前工作中使用的分析。
英文摘要：
We continue the work started in Part I of this article, showing how the addition of noise can stabilize an otherwise unstable system. The analysis makes use of nearly optimal Lyapunov functions. In this continuation, we remove the main limiting assumption of Part I by an inductive procedure as well as establish a lower bound which shows that our construction is radially sharp. We also prove a version of Peskir's \cite{Peskir_07} generalized Tanaka formula adapted to patching together Lyapunov functions. This greatly simplifies the analysis used in previous works.
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