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.

翻译：众所周知,在适当的正常条件下,带有分数参数的归正分数分数过程(d$)与以1/2美元计分数的Brownian动议($>1/2美元)不完全吻合。我们显示,对于任何非负整数的M美元,单数分数过程的衍生物(mm=0,1,\dts,美元)与分数参数的归正分数过程($d$)的M$,都与分数的分数运动的相应衍生物(d$)不完全吻合。举例来说,我们把结果应用到多折数矢量矢量自动递减模型中分数矢量的无症状分布上。