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We consider equidistant Riemann approximations of stochastic integrals$\int_0^T f(B^H_s)dB^H_s$ with respect to the fractional Brownian motion with$H>\frac12$, where $f$ is an arbitrary function of locally bounded variation,hence possibly possessing discontinuities. We prove that properly normalisedapproximation error converge in the $L^2$-topology to a functional of the localtime, and we provide rate of convergence for this approximation. As such, ourresults complements some recent advances on the topic as well as provides newmethods for simulation of local times.

Discretisation error for stochastic integrals with respect to the fractional Brownian motion with discontinuous integrands and local times