Rate of convergence for discretization of integrals with respect to Fractional Brownian motion

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In this article, an uniform discretization of stochastic integrals ∫₀¹ f'-(Bₜ) Bₜ, with respect to fractional Brownian motion with Hurst parameter H ∈ (1/2,1), for a large class of convex functions f is considered. In Statistics & Decisions, 27, 129-143, for any convex function f, the almost sure convergence of uniform discretization to such stochastic integral is proved. Here we prove Lʳ- 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 as closely as possible to H - 1/2.