Scaling limit for escapes from unstable equilibria in the vanishing noise limit: Nontrivial Jordan block case
Scaling limit for escapes from unstable equilibria in the vanishing noise limit: Nontrivial Jordan block case
复制标题
在消失的噪声极限中逃离不稳定平衡的缩放极限：非平凡的 Jordan 块情况
DOI：
10.1142/s0219493719500229
复制
发表时间：
2017
影响因子：
1.1
通讯作者：
Zsolt Pajor
中科院分区：
文献类型：
--
作者：
Yuri Bakhtin;Zsolt Pajor
考虑了非线性动力系统在不稳定临界点附近的白噪声摄动，其线性化由全维Jordan块给出。对于相关的出口问题，我们研究了在噪声消失极限下出口位置和出口时间的联合极限行为。出口通常发生在与特征方向相关的两个特殊确定性点之一附近，并且我们在出口点的展开中获得了更多项。前导校正项在噪声量级上是确定的和对数的，而随机余数满足标度限制。
We consider white noise perturbations of a nonlinear dynamical system in the neighborhood of an unstable critical point with linearization given by a Jordan block of full dimension. For the associated exit problem, we study the joint limiting behavior of the exit location and exit time, in the vanishing noise limit. The exit typically happens near one of two special deterministic points associated with the eigendirection, and we obtain several more terms in the expansion for the exit point. The leading correction term is deterministic and logarithmic in the noise magnitude, while the random remainder satisfies a scaling limit.