The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of the diffusion parameter and an approximate maximum likelihood estimator of the drift parameter based on a discretized likelihood function have been established in a suitable scaling regime involving the time-gap between the observations and the overall time span. Our framework is more general than that typically considered in the literature and, thus, has the potential to be applicable to a wider range of stochastic models.

翻译：本文研究了由布朗运动驱动的多维随机微分方程基于高频离散数据的估计量的渐近性质。在涉及观测时间间隔与总时间跨度的适当标度体系下，我们建立了一类扩散参数估计量的相合性与中心极限性质，以及基于离散化似然函数的漂移参数近似极大似然估计量的性质。我们的框架比文献中通常考虑的更为一般，因此具有应用于更广泛随机模型的潜力。