论文标题
具有周期性平均值的非邻分别分数Ornstein-Uhlenbeck的统计分析
Statistical analysis of the non-ergodic fractional Ornstein-Uhlenbeck process with periodic mean
论文作者
论文摘要
考虑一个周期性的，均值的ornstein-uhlenbeck过程$ x = \ {x_t，t $ d x_ {t x_ {t x_ {t} = \ left（l（t）+αx_{t）+αx_{t） $ l（t）= \ sum_ {i = 1}^{p}μ_iϕ_i（t）$是一个周期性的参数函数，$ \ {b^h_t，t \ geq0 \} $是hurst paramite $ \ frac12 \ leq leq heq h <1 $ $的分数布朗的运动。在$（μ_1，\ ldots，μ_p，α）$的“ ergodic”情况$α<0 $中，基于$ x $的连续观察的参数估计已在Dehling等人中考虑。 \ cite {dfk}，以及在Dehling等人中。 \ cite {dfw}分别为$ h = \ frac12 $和$ \ frac12 <h <1 $。在本文中，我们考虑了“非凝技术”案例$α> 0 $，对于所有$ \ frac12 \ leq h <1 $。当观察到$ x $的整个轨迹时，我们分析了$（μ_1，\ ldots，μ_p，α）$的估计器的强一致性和渐近分布。
Consider a periodic, mean-reverting Ornstein-Uhlenbeck process $X=\{X_t,t\geq0\}$ of the form $d X_{t}=\left(L(t)+αX_{t}\right) d t+ dB^H_{t}, \quad t \geq 0$, where $L(t)=\sum_{i=1}^{p}μ_iϕ_i (t)$ is a periodic parametric function, and $\{B^H_t,t\geq0\}$ is a fractional Brownian motion of Hurst parameter $\frac12\leq H<1$. In the "ergodic" case $α<0$, the parametric estimation of $(μ_1,\ldots,μ_p,α)$ based on continuous-time observation of $X$ has been considered in Dehling et al. \cite{DFK}, and in Dehling et al. \cite{DFW} for $H=\frac12$, and $\frac12<H<1$, respectively. In this paper we consider the "non-ergodic" case $α>0$, and for all $\frac12\leq H<1$. We analyze the strong consistency and the asymptotic distribution for the estimator of $(μ_1,\ldots,μ_p,α)$ when the whole trajectory of $X$ is observed.
