  In this paper, we consider an inference problem for an Ornstein-Uhlenbeck
process driven by a general one-dimensional centered Gaussian process
$(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance
function $ R(t,\, s)=\mathbb{E}[G_t G_s]$ can be decomposed into two parts, one
of which coincides with that of fractional Brownian motion and the other is
bounded by $(ts)^{\beta-1}$ up to a constant factor. This condition is valid
for a class of continuous Gaussian processes that fails to be self-similar or
have stationary increments. Some examples include the subfractional Brownian
motion and the bi-fractional Brownian motion. Under this assumption, we study
the parameter estimation for drift parameter in the Ornstein-Uhlenbeck process
driven by the Gaussian noise $(G_t)_{t\ge 0}$. For the least squares estimator
and the second moment estimator constructed from the continuous observations,
we prove the strong consistency and the asympotic normality, and obtain the
Berry-Ess\'{e}en bounds. The proof is based on the inner product's
representation of the Hilbert space $\mathfrak{H}$ associated with the Gaussian
noise $(G_t)_{t\ge 0}$, and the estimation of the inner product based on the
results of the Hilbert space associated with the fractional Brownian motion.

Probability