Probability density of fractional Brownian motion and the fractional Langevin equation with absorbing walls

Abstract Fractional Brownian motion and the fractional Langevin equation are models of anomalous diffusion processes characterized by long-range power-law correlations in time. We employ large-scale computer simulations to study these two geometries, (i) spreading particles on a semi-infinite domain with an absorbing wall at one end (ii) stationary state finite interval boundaries both ends source center. demonstrate that probability density other properties can be mapped onto corresponding quantities driven same noise if exponent α is replaced 2 − . In contrast, reflecting were recently shown differ from each qualitatively. Specifically, we find close behaves as P ( x ) ∼ κ distance long-time limit. case motion, varies = 2/ 1, was conjectured previously. also compare our simulation results perturbative analytical approach motion.