  We study large deviations for the time average of the Ornstein-Uhlenbeck
process raised to an arbitrary power. We prove that beyond a critical value,
large deviations are subexponential in time, with a non-convex rate function
whose main coefficient is given by the solution to a Hamilton-Jacobi problem.
Although a similar problem was addressed in a recent work, the originality of
the paper is to provide a short, self-contained proof of this result through a
couple of standard large deviations arguments.
