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

We prove the weak convergence in C([0,T])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, BHBH, with Hurst parameter H>1/2H>1/2, to the law of the corresponding multiple integral with respect to BH0BH0, when HH tends to H0∈[1/2,1)H0∈[1/2,1).