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

We numerically study fractional Brownian motion (fBm) with an absorbing boundary at the origin for selected values of the Hurst exponent Hε[0,1]. Using a Monte Carlo sampling technique, we are able to numerically generate these fBm processes at discrete times for up to 10(7) time steps, even for values as small as H=1/4. The results are compatible with previous analytical results that suggest that the distribution of (rescaled) endpoints y follow a power law P(+)(y)~y(φ) with φ=(1-H)/H, even for small values of H. Furthermore, for H=0.5 we study analytically the finite-length corrections to first order, namely a plateau of P(+)(y) for y→0 which decreases with increasing process length. These corrections are compatible with our numerical results.