Power variation of some integral fractional processes

We consider the asymptotic behaviour of the realized power variation of processes of the formÐ t 0 us dB H s, where B H is a fractional Brownian motion with Hurst parameter H 2 (0, 1), and u is a process with finite q-variation, q, 1=(1 H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter