论文标题
最小二乘估计非连加权分数Ornstein-uhlenbeck的一般参数的过程
Least squares estimation for non-ergodic weighted fractional Ornstein-Uhlenbeck process of general parameters
论文作者
论文摘要
令$ b^{a，b}：= \ {b_t^{a，b}，t \ geq0 \} $是加权分数的参数的分数brownian运动$ a> -1 $，$ | b | b | <1 $，$ | b | b | <a+1 $。我们考虑了一种至少方形型方法来估计加权分数Ornstein-uhlenbeck的漂移参数$θ> 0 $ $ x：= \ {x_t，t \ geq0 \} $由$ x_0 = 0; \ dx_t =θx_tdt+db_t^{a，b} $。 在这项工作中，我们为$ x $的$θ$和离散时间观察提供最小二乘型估计器。研究了所有$（a，b）$的强大一致性和渐近行为，以使$ a> -1 $，$ | b | <1 $，$ | b | <a+1 $。在这里，我们扩展了\ cite {syy2，syy}的结果（resp。\ cite {csc}），其中证明了强的一致性和渐近分布 $ - \ frac12 <a <0 $，$ -a <b <a+1 $（$ -1 <a <0 $，$ -a <b <a+1 $）。
Let $B^{a,b}:=\{B_t^{a,b},t\geq0\}$ be a weighted fractional Brownian motion of parameters $a>-1$, $|b|<1$, $|b|<a+1$. We consider a least square-type method to estimate the drift parameter $θ>0$ of the weighted fractional Ornstein-Uhlenbeck process $X:=\{X_t,t\geq0\}$ defined by $X_0=0; \ dX_t=θX_tdt+dB_t^{a,b}$. In this work, we provide least squares-type estimators for $θ$ based continuous-time and discrete-time observations of $X$. The strong consistency and the asymptotic behavior in distribution of the estimators are studied for all $(a,b)$ such that $a>-1$, $|b|<1$, $|b|<a+1$. Here we extend the results of \cite{SYY2,SYY} (resp. \cite{CSC}), where the strong consistency and the asymptotic distribution of the estimators are proved for $-\frac12<a<0$, $-a<b<a+1$ (resp. $-1<a<0$, $-a<b<a+1$).
