We will consider the following stochastic differential equation (SDE): \begin{equation} X_t=X_0+\int_0^tb(X_s,\theta_0)ds+\sigma B_t,~~~t\in(0,T], \end{equation} where $\{B_t\}_{t\ge 0}$ is a fractional Brownian motion with Hurst index $H\in(1/2,1)$, $\theta_0$ is a parameter that contains a bounded and open convex subset $\Theta\subset\mathbb{R}^d$, $\{b(\cdot,\theta),\theta\in\Theta\}$ is a family of drift coefficients with $b(\cdot,\theta):\mathbb{R}\rightarrow\mathbb{R}$, and $\sigma\in\mathbb{R}$ is assumed to be the known diffusion coefficient.
翻译:我们将考虑以下分等式(SDE):\ begin{equation} X_t=X_0 ⁇ int_0 ⁇ tb(X_s,\theta_0)ds\sgma B_t,\t\in(0,T),\end{equation} ${B_t\ge 0},\end{equation$是分数的棕色运动,具有赫斯特指数$H\in( 1/2, 1) $, $\theta_0$(0美元) 是一个包含约束和开放的 convex子集 $Theta\subet\subs\mathbb{R} 的参数,$_b(cdot,\theta),\theta\in\in\\equ$(美元) 是带有$b(\\cdot,\theta) 的漂浮系数的一组 :\mathb{rtb{r\\\\\\mathb{R}$\\\\\ lade lade supp}