Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion

In this article, a uniform discretization of stochastic integrals integral(1)(0)integral'-(B-t)dB(t), where denotes the fractional Brownian motion with Hurst parameter , is considered for a large class of convex functions . In Azmoodeh et al. (Stat Decis 27:129-143, 2010), for any convex function , the almost sure convergence of uniform discretization to such stochastic integral is proved. Here, we prove -convergence of uniform discretization to stochastic integral. In addition, we obtain a rate of convergence. It turns out that the rate of convergence can be brought arbitrarily close to H = 1/2.