We consider parametric estimation for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main targets are the drift parameter $\alpha$ and the diffusion parameter $\beta$. In this paper, we propose two types of adaptive estimators for $(\alpha,\beta)$ and show their asymptotic properties under $\varepsilon\to0$, $n\to\infty$ and the balance condition that $(\varepsilon n^\rho)^{-1} =O(1)$ for some $\rho\ge 1/2$. In simulation studies, we examine and compare asymptotic behaviors of the two kinds of adaptive estimators. Moreover, we treat the SIR model which describes a simple epidemic spread for a biological application.

翻译：我们从离散观测中考虑对具有小分散参数的多维扩散过程的参数估计值。对于对扩散过程的参数估计值,主要目标是漂移参数值$alpha$和扩散参数值$\beta$。在本文中,我们提出两种类型的适应性估计值为$(alpha,\beta)$,并显示其无症状特性在$\varepsilont$至0美元、$n\to\inty$和平衡条件($(varepsilon n ⁇ rho)- ⁇ 1}=$(O(1)$,大约为$\rho\ge 1/2美元)。在模拟研究中,我们检查并比较两种类型的适应性估计值的无症状行为。此外,我们处理SIR模型,该模型描述生物应用的简单流行病扩散。