Recent progress on the small parameter exit problem
Recent progress on the small parameter exit problem
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小参数退出问题的最新进展
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
M. Day
中科院分区：
文献类型：
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作者：
M. Day
在本文中，我们将汇集一些最近的结果S。J. Sheu，T.A.达登和我们自己的小参数出口问题，并发展他们的应用A. D. Wentzell和M.I.佛雷德林本文研究了具有渐近小随机扰动的动力系统的指数稳定临界点的吸引域的出口分布的渐近行为。Day和达登关于所谓准势函数的正则性的最新结果使S.关于平衡密度的渐近行为。将这些结果应用于出口问题，通过它与平衡密度的联系，[2]，我们得到了关于出口问题的一个新定理：定理4如下。这个定理包含了以前的结果，并推广了Matkowksi-Schuss-Kamin方法的结论，从光滑到非光滑拟势函数。在所有情况下，退出问题都被简化为...
In this paper we will bring together some recent results of S.-J. Sheu, T.A. Darden and ourselves and develop their application to the small parameter exit problem of A.D. Wentzell and M.I. Freidlin. This problem concerns the asymptotic behavior of the exit distribution from a domain of attraction for an exponentially stable critical point of a dynamical system with an asymptotically small random perturbation. Recent results of Day and Darden on regularity properties of the so-called quasipotential function allow certain improvements and generalizations to be made in the work fo S.-J. Sheu on the asyptotic behavior of the equilibrium density. Applying these results to the exit problem through its connection with the equilibrium density, [2], we obtain a new theorem on the exit problem: Theorem 4 below. This theorem subsumes previous results and generalizes the conclusion of the Matkowksi-Schuss-Kamin approach from smooth to nonsmooth quasipotental functions. In all cases the exit problem is reduced to the...