Approximation of the finite dimensional distributions of multiple fractional integrals

We construct a family I n ε ( f ) t of continuous stochastic processes that converges in the sense of finite dimensional distributions to a multiple Wiener–Itô integral I n H ( f 1 [ 0 , t ] ⊗ n ) with respect to the fractional Brownian motion. We assume that H > 1 2 and we prove our approximation result for the integrands f in a rather general class.