WEAK CONVERGENCE TO DERIVATIVES OF FRACTIONAL BROWNIAN MOTION

It is well known that, under suitable regularity conditions, the normalized fractional process with parameter d converges weakly to Brownian motion (fBm) for $d>\frac {1}{2}$ . We show any nonnegative integer M , derivatives of order $m=0,1,\dots ,M$ respect jointly converge corresponding fBm. As an illustration, we apply results asymptotic distribution score vectors in multifractional vector autoregressive model.