Smoluchowski-Kramers approximation and large deviations for infinite dimensional non-gradient systems with applications to the exit problem
Smoluchowski-Kramers approximation and large deviations for infinite dimensional non-gradient systems with applications to the exit problem
复制标题
无限维非梯度系统的 Smoluchowski-Kramers 近似和大偏差及其在退出问题中的应用
DOI：
10.1214/15-aop1029
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
M. Salins
中科院分区：
文献类型：
--
作者：
S. Cerrai;M. Salins
本文研究了一类广义阻尼半线性随机波动方程的拟位势。我们表明，作为质量的密度收敛到零，准潜在的下确界相对于所有可能的速度收敛到相应的随机热方程的准潜在的，从零质量极限。这特别表明，Smoluchowski-Kramers近似不仅对小时间有效，而且在零噪声限制制度下，可以用来近似长时间的行为，如退出时间和退出吸引盆的位置。
In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that, as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular that the Smoluchowski-Kramers approximation is not only valid for small time, but, in the zero noise limit regime, can be used to approximate long-time behaviors such as exit time and exit place from a basin of attraction.