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              <p>In this article, we give sharp bounds for the Euler- and trapezoidal discretization of the Levy area associated to a d-dimensional fractional Brownian motion. We show that there are three different regimes for the exact root mean-square convergence rate of the Euler scheme. For H&lt;3/4 the exact convergence rate is n^{-2H+1/2}, where n denotes the number of the discretization subintervals, while for H=3/4 it is n^{-1} (log(n))^{1/2} and for H&gt;3/4 the exact rate is n^{-1}. Moreover, the trapezoidal scheme has exact convergence rate n^{-2H+1/2} for H&gt;1/2. Finally, we also derive the asymptotic error distribution of the Euler scheme. For H lesser than 3/4 one obtains a Gaussian limit, while for H&gt;3/4 the limit distribution is of Rosenblatt type.</p>
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