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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 {Bt}t0\{B_t\}_{t\ge 0} is a fractional Brownian motion with Hurst index H(1/2,1)H\in(1/2,1), θ0\theta_0 is a parameter that contains a bounded and open convex subset ΘRd\Theta\subset\mathbb{R}^d, {b(,θ),θΘ}\{b(\cdot,\theta),\theta\in\Theta\} is a family of drift coefficients with b(,θ):RRb(\cdot,\theta):\mathbb{R}\rightarrow\mathbb{R}, and σR\sigma\in\mathbb{R} is assumed to be the known diffusion coefficient.

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