  We study the full nonequilibirum steady state distribution
$P_{\text{st}}\left(X\right)$ of the position $X$ of a damped particle confined
in a harmonic trapping potential and experiencing active noise, whose
correlation time $\tau_c$ is assumed to be very short. Typical fluctuations of
$X$ are governed by a Boltzmann distribution with an effective temperature that
is found by approximating the noise as white Gaussian thermal noise. However,
large deviations of $X$ are described by a non-Boltzmann steady-state
distribution. We find that, in the limit $\tau_c \to 0$, they display the
scaling behavior $P_{\text{st}}\left(X\right)\sim
e^{-s\left(X\right)/\tau_{c}}$, where $s\left(X\right)$ is the large-deviation
function. We obtain an expression for $s\left(X\right)$ for a general active
noise, and calculate it exactly for the particular case of telegraphic
(dichotomous) noise.
