Statistics of the first passage area functional for an Ornstein-Uhlenbeck process

Abstract: 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.