Continuity in the Hurst parameter of the law of the symmetric integral with respect to the fractional Brownian motion

We prove the convergence in law, in the space of continuous functions C ( [ 0 , T ] ) , of the Russo–Vallois symmetric integral of a non-adapted process with respect to the fractional Brownian motion with Hurst parameter H > 1 / 2 to the Russo–Vallois symmetric integral with respect to the fractional Brownian motion with parameter H 0 , when H tends to H 0 ∈ [ 1 / 2 , 1 ) .