Continuity with respect to the Hurst parameter of the laws of the multiple fractional integrals

We prove the weak convergence in C ( [ 0 , T ] ) of the laws of the Itô and Stratonovich multiple integrals of some classes of deterministic functions with respect to the fractional Brownian motion, B H , with Hurst parameter H > 1 / 2 , to the law of the corresponding multiple integral with respect to B H 0 , when H tends to H 0 ∈ [ 1 / 2 , 1 ) .