Tempered Fractional Brownian Motion with Reflecting Walls

Fractional Brownian Motion (FBM) is a Gaussian stochastic process with long-range correlations and a paradigmatic model for anomalous diffusion. For FBM confined by reflecting boundaries, recent work [1] demonstrated unusual accumulation and depletion of particles close to the walls. In many applications of FBM to physics, chemistry, and beyond, the long-range correlations are cut off (tempered) beyond a certain time scale [2]. Here, we study the behavior of tempered FBM in the presence of reflecting walls. More specifically, we analyze the probability density of tempered FBM on a one-dimensional interval between two reflecting walls.
[1] A.H.O. Wada and T. Vojta, Phys. Rev. E 97, 020102 (2018)
[2] D. Molina-Garcia et al., New J. Phys. 20, 103027 (2018)