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：本文涉及以 $\ mathbb{R<unk> \\ times\ mathb{R<unk> n$ 表示的以 $AD(1, n) 表示的对松散扩散的全球参数估计问题, 美元是一个正整数, 是Duffie 等人在 [14] 中引入的松散扩散子分类。 $AD(1, n) 模式可以适用于债券和股票期权的价格, 用于Vasicek、 Cox- Ingersoll- Ross 和 Heston 模型。 我们的第一个结果是根据亚临界、 关键和超临界案例对 $AD(1, n) 进程进行分类。 然后, 我们给这个模型的定位性和直观性理论, 我们为在亚临界和特殊超临界案例中的最大可能性估计器的设定无症状特性。</s>