  The survival probability for a periodic non-autonomous Ornstein-Uhlenbeck
process is calculated analytically using two different methods. The first uses
an asymptotic approach. We treat the associated Kolmogorov Backward Equation
with an absorbing boundary by dividing the domain into an interior region,
centered around the origin, and a "boundary layer" near the absorbing boundary.
In each region we determine the leading-order analytical solutions, and
construct a uniformly valid solution over the entire domain using asymptotic
matching. In the second method we examine the integral relationship between the
probability density function and the mean first passage time probability
density function. These allow us to determine approximate analytical forms for
the exit rate. The validity of the solutions derived from both methods is
assessed numerically, and we find the asymptotic method to be superior.
