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

An approximate maximum likelihood estimator of drift parameters in a multidimensional diffusion model