发表机构
Freie Universität Berlin; Tulane University; University of Amsterdam; Universität Bayreuth（柏林自由大学; 杜兰大学; 阿姆斯特丹大学; 拜罗伊特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究随机惯性现象，推导积分公式判定噪声延长逃逸时间的条件，并证明其为平均逃逸时间的零噪声导数，通过鞍点与弛豫振荡器示例验证不稳定方向主导逃逸时随机惯性出现。
AI 中文摘要
受大气建模中观测现象的启发，我们研究了“随机惯性”效应：在某些动力系统中，小噪声会诱导轨迹在状态空间中一个动态关键子集内停留的时间比纯确定性情形更长。在对随机微分方程的温和一般假设下，我们推导出一个沿确定性轨迹的积分公式，其符号为随机惯性发生提供了充分条件。排除具有无限逃逸时间的开集情形，并假设扩散项一致椭圆，我们进一步将该积分公式识别为平均逃逸时间在零噪声处的导数。证明关键使用了Dynkin公式以及对Freidlin-Wentzell理论的适当改编。我们提出了一种计算该积分公式的算法方法，并通过鞍点和弛豫振荡器的例子，展示了以下启发式结论：随机惯性出现在存在一个不稳定方向且该方向主要主导逃逸动力学的情形中。
英文摘要
Motivated by observations in atmospheric modelling, we investigate the effect of ``stochastic inertia'': in certain dynamical systems, small noise induces trajectories to stay longer in a dynamically critical subset of state space than in the purely deterministic situation. Under mild general assumptions on the stochastic differential equation, we derive an integral formula along deterministic trajectories whose sign provides a sufficient condition for the occurrence of stochastic inertia. Excluding situations with open sets of infinite escape times and assuming uniformly elliptic diffusion, we additionally identify this integral formula as the zero noise derivative of the average escape time. The proofs make crucial use of Dynkin's formula and suitable adaptations of Freidlin--Wentzell theory. We present an algorithmic approach to compute the integral formula and, by examples of saddle points and relaxation oscillators, demonstrate the following heuristic: stochastic inertia appears in the presence of an unstable direction that predominantly leads the escape dynamics.
