Stochastic integration with respect to fractional Brownian motion

The purpose of this paper is to construct a stochastic integral with respect to fractional Brownian motion W-H, for every value of the Hurst index H is an element of (0, 1), as the limit of integrals with respect to semimartingales approximating W-H. We relate this construction to former integration theory (pathwise and stochastic), and in particular we give, for H > 1/4 a precise interpretation of Privault's Ito formula [12]. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.