  In Chen and Zhou 2021, they 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 $(ts)^{H-1}$ with $H\in (\frac12,\,1)$, up to a
constant factor.
  In this paper, we investigate the same problem but with the assumption of
$H\in (0,\,\frac12)$. It is well known that there is a significant difference
between the Hilbert space associated with the fractional Gaussian processes in
the case of $H\in (\frac12, 1)$ and that of $H\in (0, \frac12)$. The starting
point of this paper is a new relationship between the inner product of
$\mathfrak{H}$ associated with the Gaussian process $(G_t)_{t\ge 0}$ and that
of the Hilbert space $\mathfrak{H}_1$ associated with the fractional Brownian
motion $(B^{H}_t)_{t\ge 0}$. Then we prove the strong consistency with $H\in
(0, \frac12)$, and the asymptotic normality and the Berry-Ess\'{e}en bounds
with $H\in (0,\frac38)$ for both the least squares estimator and the moment
estimator of the drift parameter constructed from the continuous observations.
A good many inequality estimates are involved in and we also make use of the
estimation of the inner product based on the results of $\mathfrak{H}_1$ in Hu,
Nualart and Zhou 2019.
