  We consider the statistical properties of a non-falling trajectory in the
Whitney problem of an inverted pendulum excited by an external force. In the
case when the external force is white noise, we recently found the
instantaneous distribution function of the pendulum angle and velocity over an
infinite time interval using a transfer-matrix analysis of the supersymmetric
field theory. Here, we generalize our approach to the case of finite time
intervals and multipoint correlation functions. Using the developed formalism,
we calculate the Lyapunov exponent, which determines the decay rate of
correlations on a non-falling trajectory.
