论文标题
在离散观测下的分数Ornstein-Uhlenbeck模型中所有参数的估计
Estimation Of all parameters in the Fractional Ornstein-Uhlenbeck model under discrete observations
论文作者
论文摘要
让Ornstein -uhlenbeck进程$（x_t）_ {t \ ge0} $由$ dx_t =-θx_tdt dt dt dt +σdb_t^{h}驱动的分数布朗运动$ b^{h} $驱动 $ t_k = kh $，$ k = 0、1、2，\ cdots，2n+2 $。我们提出了Ergodic类型的统计估计器$ \hatθ_n$，$ \ hat H_n $和$ \ hatσ_n$，以估计所有参数$θ$，$ h $和$ h $和$σ$同时在上述Ornstein-Uhlenbeck模型中。我们证明了估计量的强烈一致性和收敛速度。步长$ h $可以任意固定，并且不会被迫零，这通常是现实。要使用的工具是广义力矩方法（通过厄戈德定理）和malliavin conculus。
Let the Ornstein-Uhlenbeck process $(X_t)_{t\ge0}$ driven by a fractional Brownian motion $B^{H }$, described by $dX_t = -θX_t dt + σdB_t^{H }$ be observed at discrete time instants $t_k=kh$, $k=0, 1, 2, \cdots, 2n+2 $. We propose ergodic type statistical estimators $\hat θ_n $, $\hat H_n $ and $\hat σ_n $ to estimate all the parameters $θ$, $H $ and $σ$ in the above Ornstein-Uhlenbeck model simultaneously. We prove the strong consistence and the rate of convergence of the estimators. The step size $h$ can be arbitrarily fixed and will not be forced to go zero, which is usually a reality. The tools to use are the generalized moment approach (via ergodic theorem) and the Malliavin calculus.
