We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a logarithmic deterministic term and a random correction converging in distribution. Thus, this setting is in the universality class of the unstable equilibrium exit under small white-noise perturbations.

中文翻译：

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不稳定平衡附近具有快速随机切换的动力系统的退出时间渐近

我们考虑在平均漂移的不稳定平衡点附近随机切换的一维系统的退出问题。在无限切换速率限制中，我们表明退出时间满足具有对数确定性项和分布收敛的随机校正的限制定理。因此，该设置属于小白噪声扰动下不稳定平衡出口的普遍性类。