强阻尼Langevin方程的大偏差
Large Deviations for the Langevin equation with strong damping
摘要：
我们研究了具有$\e^{-1}$阶阻尼和$1$阶噪声的朗之万动力学中的大偏差，作为$\e\downarrow 0$。阻尼系数被假定为与状态有关。我们首先进行了时间的变化，然后，我们使用弱收敛方法的大偏差和他们的等价配方的拉普拉斯原理，以确定良好的作用功能。这些结果的一些应用，从一个区域的出口问题和波前传播的一类合适的反应扩散方程被认为是。
英文摘要：
We study large deviations in the Langevin dynamics, with damping of order $\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient is assumed to be state dependent. We proceed first with a change of time and then, we use a weak convergence approach to large deviations and their equivalent formulation in terms of the Laplace principle, to determine the good action functional. Some applications of these results to the exit problem from a domain and to the wave front propagation for a suitable class of reaction diffusion equations are considered.
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