  We present a path integral calculation of the probability distribution
associated with the time-integrated moments of the Ornstein-Uhlenbeck process
that includes the Gaussian prefactor in addition to the dominant path or
instanton term obtained in the low-noise limit. The instanton term was obtained
recently [D. Nickelsen, H. Touchette, Phys. Rev. Lett. 121, 090602 (2018)] and
shows that the large deviations of the time-integrated moments are anomalous in
the sense that the logarithm of their distribution scales nonlinearly with the
integration time. The Gaussian prefactor gives a correction to the low-noise
approximation and leads us to define an instanton variance giving some insights
as to how anomalous large deviations are created in time. The results are
compared with simulations based on importance sampling, extending our previous
results based on direct Monte Carlo simulations. We conclude by explaining why
many of the standard analytical and numerical methods of large deviation theory
fail in the case of anomalous large deviations.
