论文标题
浆果eséen绑定了第二类的漂移估算的漂移估计
Berry-Esséen bound for drift estimation of fractional Ornstein Uhlenbeck process of second kind
论文作者
论文摘要
在本文中，我们考虑第二种的Ornstein -uhlenbeck过程，该过程定义为方程的解决方案$ dx_ {t} =-αx_{t} dt+dy_ {t}^{（1）}， \ \ x_ {0} = 0 $，其中$ y_ {t}^{（1）}：= \ int_ {0}^{t}^{t} e^{ - s} db^h_ {a_ {a_ {s}} $ with $ a_ {t}带有Hurst参数的Brownian Motion $ h \ in（\ frac12,1）$，而$α> 0 $是未知参数。我们在kolmogorov距离中获得了上限$ o（1/\ sqrt {t}）$，以根据连续观察$ \ \ \ \ {x_t，t \ in [0，t] \} $，as $ t \ frightrow \ frirtarow \ frircrow \ frircty $ \ frive \ fircty $ \ frive progains $α$的正常近似。我们的方法基于\ cite {kp-jva}的工作，该方法是使用malliavin conculus和Stein方法的组合证明的，以实现正常近似。
In the present paper we consider the Ornstein-Uhlenbeck process of the second kind defined as solution to the equation $dX_{t} = -αX_{t}dt+dY_{t}^{(1)}, \ \ X_{0}=0$, where $Y_{t}^{(1)}:=\int_{0}^{t}e^{-s}dB^H_{a_{s}}$ with $a_{t}=He^{\frac{t}{H}}$, and $B^H$ is a fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$, whereas $α>0$ is unknown parameter to be estimated. We obtain the upper bound $O(1/\sqrt{T})$ in Kolmogorov distance for normal approximation of the least squares estimator of the drift parameter $α$ on the basis of the continuous observation $\{X_t,t\in[0,T]\}$, as $T\rightarrow\infty$. Our method is based on the work of \cite{kp-JVA}, which is proved using a combination of Malliavin calculus and Stein's method for normal approximation.
