  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.
