This paper deals with the problem of global parameter estimation of affine diffusions in $\mathbb{R}_+ \times \mathbb{R}^n$ denoted by $AD(1, n)$ where $n$ is a positive integer which is a subclass of affine diffusions introduced by Duffie et al in [14]. The $AD(1, n)$ model can be applied to the pricing of bond and stock options, which is illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models. Our first result is about the classification of $AD(1, n)$ processes according to the subcritical, critical and supercritical cases. Then, we give the stationarity and the ergodicity theorems of this model and we establish asymptotic properties for the maximum likelihood estimator in both subcritical and a special supercritical cases.

翻译：本文研究 $\mathbb{R}_+ \times \mathbb{R}^n$ 上仿射扩散过程（记为 $AD(1, n)$，其中 $n$ 为正整数）的全局参数估计问题。该模型是 Duffie 等人在文献[14]中引入的仿射扩散子类，可应用于债券与股票期权的定价，并通过 Vasicek、Cox-Ingersoll-Ross 和 Heston 模型加以说明。本文首先根据次临界、临界和超临界情形对 $AD(1, n)$ 过程进行分类，继而给出该模型的平稳性与遍历性定理，并建立次临界及特殊超临界情形下极大似然估计的渐近性质。