Fractional Brownian Motion with an Absorbing Wall

Fractional Brownian motion, a random walk with long-time power-law correlations between its steps, is a prototypical model for anomalous diffusion. We employ large scale Monte Carlo simulations to investigate fractional Brownian motion in the presence of an absorbing wall. In the limit of vanishing correlations, our findings reproduce the well-known results for normal diffusion. In contrast, the interplay between the absorbing wall and the long-range power correlations leads to a singular probability density close to the wall. We compare our results to those of Brownian Motion in the presence of a reflecting wall [1], and we discuss implications of our results.
[1] A.H.O Wada and T. Vojta, Phys. Rev. E 97, 020102 (2018)