论文标题
在随机微分方程中的幂定律依赖性
Power law dependence in a random differential equation
论文作者
论文摘要
本文研究了随机开关扰动的随机微分方程。我们探讨了均衡状态的最大位移如何取决于{}随机开关的时间序列的统计属性。我们显示了位移上限与随机扰动开关的频率之间的功率定律依赖性，并且幂律依赖性的斜率取决于开关时间之间间隔的特定分布。此结果{建议}在随机扰动下频率调制与振幅调制之间的定量连接。
This paper studies a random differential equation with random switch perturbations. We explore how the maximum displacement from the equilibrium state depends on the statistical properties of time series of {the} random switches. We show a power law dependence between the upper bound of displacement and the frequency of random perturbation switches, and the slope of power law dependence is dependent on the specific distribution of the intervals between switching times. This result {suggests} a quantitative connection between frequency modulation and amplitude modulation under random perturbations.
