论文标题
Ornstein-Uhlenbeck过程的第一个通道区域的统计数据
Statistics of the first passage area functional for an Ornstein-Uhlenbeck process
论文作者
论文摘要
我们考虑由Ornstein-uhlenbeck过程的积分定义的区域功能，该过程从给定值开始，并在首先达到零（其平衡水平）时结束。为基础面积概率分布的平均值，方差，偏度和峰度提供了确切的结果，以及该区域与第一个通道时间之间的协方差和相关性。除其他外，分析表明，在弱噪声限制中，面积分布在差异上是渐近正常的，这与第一个通道时间分布相反。指示各种应用。
We consider the area functional defined by the integral of an Ornstein-Uhlenbeck process which starts from a given value and ends at the time it first reaches zero (its equilibrium level). Exact results are presented for the mean, variance, skewness and kurtosis of the underlying area probability distribution, together with the covariance and correlation between the area and the first passage time. Amongst other things, the analysis demonstrates that the area distribution is asymptotically normal in the weak noise limit, which stands in contrast to the first passage time distribution. Various applications are indicated.
