Asymptotic normality of least squares estimators to stochastic differential equations driven by fractional Brownian motions

Abstract

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.