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. Among 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.

中文翻译：

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Ornstein–Uhlenbeck过程的第一个通道区域的统计数据

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，直到其首次达到零（其平衡水平）时结束。给出了有关潜在区域概率分布的均值，方差，偏度和峰度的精确结果，以及区域与首次通过时间之间的协方差和相关性。分析尤其表明，该区域分布在弱噪声限制中是渐近正态的，这与第一次通过时间分布相反。指出了各种应用。