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

Parameter estimation for an Ornstein-Uhlenbeck Process driven by a general Gaussian noise