Weak symmetric integrals with respect to the fractional Brownian motion

The aim of this paper is to establish the weak convergence, in the topology of the Skorohod space, of the .-symmetric Riemann sums for functionals of the fractional Brownian motion when the Hurst parameter takes the critical value H=(4.+2).1, where .=.(.).1 is the largest natural number satisfying .10.2j.(d.)=12j+1 for all j=0,.,..1. As a consequence, we derive a change-of-variable formula in distribution, where the correction term is a stochastic integral with respect to a Brownian motion that is independent of the fractional Brownian