WEAK CONVERGENCE TO DERIVATIVES OF FRACTIONAL BROWNIAN MOTION
证明了标准化分数过程对分数参数的各阶导数联合弱收敛到分数布朗运动的相应导数，并应用于多分数向量自回归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 (fBm) for $d>\frac {1}{2}$ . We show that, for any nonnegative 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 fBm. As an illustration, we apply the results to the asymptotic distribution of the score vectors in the multifractional vector autoregressive model.