Maximum likelihood estimation in the non-ergodic fractional Vasicek model
Maximum likelihood estimation in the non-ergodic fractional Vasicek model
复制标题
DOI：
10.15559/19-vmsta140
复制
发表时间：
2019-09
期刊：
影响因子：
--
通讯作者：
S. Lohvinenko;K. Ralchenko
中科院分区：
文献类型：
--
作者：
S. Lohvinenko;K. Ralchenko
研究了分数阶Vasicek模型，该模型由分数阶布朗运动B H$驱动，随机微分方程dX_t=（\alpha -\beta X_t）\，dt+\gamma \，dB^H_t$，$X_0 =x_0$描述，Hurst参数H\在（1/2，1）$中.本文研究了在非遍历情形下（当$\beta <0$时），对于任意的$x_0\in\mathbb{R}$，未知参数$\alpha$和$\beta$的极大似然估计，推广了Tanaka，Xiao和Yu（2019）对于特殊的$x_0=\alpha /\beta$的结果，导出了它们的渐近分布，并证明了它们的渐近独立性.
We investigate the fractional Vasicek model described by the stochastic differential equation $dX_t=(\alpha -\beta X_t)\,dt+\gamma \,dB^H_t$, $X_0=x_0$, driven by the fractional Brownian motion $B^H$ with the known Hurst parameter $H\in (1/2,1)$. We study the maximum likelihood estimators for unknown parameters $\alpha$ and $\beta$ in the non-ergodic case (when $\beta <0$) for arbitrary $x_0\in \mathbb{R}$, generalizing the result of Tanaka, Xiao and Yu (2019) for particular $x_0=\alpha /\beta$, derive their asymptotic distributions and prove their asymptotic independence.