论文标题
弱收敛到分数布朗运动的衍生物
Weak convergence to derivatives of fractional Brownian motion
论文作者
论文摘要
众所周知，在适当的规律性条件下，具有分数参数$ d $的标准化分数过程微弱地收敛到布朗尼的分数运动，$ d> 1/2 $。我们表明，对于任何非负整数$ m $，订单$ m = 0,1，\ dots，dots，m $相对于分数参数$ d $的衍生物，与分数布朗尼运动的相应衍生物相关的衍生品。作为例证，我们将结果应用于多曲线矢量自回旋模型中得分向量的渐近分布。
It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter $d$ converges weakly to fractional Brownian motion for $d>1/2$. We show that, for any non-negative integer $M$, derivatives of order $m=0,1,\dots,M$ of the normalized fractional process with respect to the fractional parameter $d$, jointly converge weakly to the corresponding derivatives of fractional Brownian motion. As an illustration we apply the results to the asymptotic distribution of the score vectors in the multifractional vector autoregressive model.
