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We study fractional Brownian motion (fBm) characterized by the Hurst exponentH. Using a Monte Carlo sampling technique, we are able to numerically generatefBm processes with an absorbing boundary at the origin at discrete times for alarge number of 10^7 time steps even for small values like H=1/4. The resultsare compatible with previous analytical results that the distribution of(rescaled) endpoints y follow a power law P(y) y^\phi with \phi=(1-H)/H, evenfor small values of H. Furthermore, for the case H=0.5 we also studyanalytically the finite-length corrections to the first order, namely a plateauof P(y) for y->0 which decreases with increasing process length. Thesecorrections are compatible with the numerical results.

Sampling fractional Brownian motion in presence of absorption: a Markov Chain method