Asymptotic error distribution for the Riemann approximation of integrals driven by fractional Brownian motion (Q2084843)

The authors show the first and second order convergence of the Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion of index \(H \geq 1/2\). In the case of second order convergence, the process obtained in the limit is a stochastic integral with respect to the Rosenblatt process if \(3/4<H<1\), and with respect to standard Brownian motion if \(1/2<H \leq 3/4\). Examples of suitable integrand processes include processes that are ``controlled'' by the increments of the integrator, fractional semimartingales, and multiple Wiener-Itô integrals.