Asymptotic Exit Time Distributions
Asymptotic Exit Time Distributions
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渐近退出时间分布
DOI：
10.1137/0142012
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发表时间：
1982
影响因子：
1.9
通讯作者：
M. Williams
中科院分区：
文献类型：
--
作者：
M. Williams
设$x(T)$是确定性动力系统在非退化白噪声作用下的随机扰动所产生的扩散。设$\tau$是$x(T)$从一个定义流有单一简单吸引临界点且在边界处向内的区域的第一个出口的时刻。前人关于确定统计量的结果包括一阶矩的渐近行为和当噪声强度趋于零时超过$t=T的包含概率的某些衰减率。在这项工作中，在势的情况下，$\tau$在这个极限下的实际渐近分布被确定为指数分布。描述这一极限的奇异摄动方程表现出Ackerberg-O‘Malley共振。
Let $x( t )$ be a diffusion resulting from the stochastic perturbation of a deterministic dynamical system by a nondegenerate white noise. Let $\tau $ be the time of first exit of $x( t )$ from a domain on which the deterministic flow has a single simple attracting critical point and is inward at the boundary. Previous results on determining the statistics of $\tau $ include the asymptotic behavior of the first moment and certain decay rates of probabilities of containment past $t = T$ as the strength of the noise tends to zero. In this work the actual asymptotic distribution of $\tau $ in this limit is determined to be exponential in the potential case. The singularly perturbed equations describing this limit exhibit Ackerberg–O’Malley resonance.