For a fixed $T$ and $k \geq 2$, a $k$-dimensional vector stochastic differential equation $dX_t=\mu(X_t, \theta)dt+\nu(X_t)dW_t,$ is studied over a time interval $[0,T]$. Vector of drift parameters $\theta$ is unknown. The dependence in $\theta$ is in general nonlinear. We prove that the difference between approximate maximum likelihood estimator of the drift parameter $\overline{\theta}_n\equiv \overline{\theta}_{n,T}$ obtained from discrete observations $(X_{i\Delta_n}, 0 \leq i \leq n)$ and maximum likelihood estimator $\hat{\theta}\equiv \hat{\theta}_T$ obtained from continuous observations $(X_t, 0\leq t\leq T)$, when $\Delta_n=T/n$ tends to zero, converges stably in law to the mixed normal random vector with covariance matrix that depends on $\hat{\theta}$ and on path $(X_t, 0 \leq t\leq T)$. The uniform ellipticity of diffusion matrix $S(x)=\nu(x)\nu(x)^T$ emerges as the main assumption on the diffusion coefficient function.

翻译：对于固定 $T$ 且 $k \geq 2$，在时间区间 $[0,T]$ 上研究 $k$ 维向量随机微分方程 $dX_t=\mu(X_t, \theta)dt+\nu(X_t)dW_t$。漂移参数向量 $\theta$ 未知，且 $\theta$ 的依赖关系一般为非线性。我们证明，由离散观测 $(X_{i\Delta_n}, 0 \leq i \leq n)$ 得到的漂移参数近似极大似然估计量 $\overline{\theta}_n\equiv \overline{\theta}_{n,T}$ 与由连续观测 $(X_t, 0\leq t\leq T)$ 得到的极大似然估计量 $\hat{\theta}\equiv \hat{\theta}_T$ 之间的差异，当 $\Delta_n=T/n$ 趋于零时，依分布稳定收敛于混合正态随机向量，其协方差矩阵依赖于 $\hat{\theta}$ 和路径 $(X_t, 0 \leq t\leq T)$。扩散矩阵 $S(x)=\nu(x)\nu(x)^T$ 的一致椭圆条件是扩散系数函数的主要假设。