Aging and confinement in subordinated fractional Brownian motion

We study the effects of aging properties of subordinated fractional Brownian motion (FBM) with drift and in harmonic confinement, when the measurement of the stochastic process starts a time t(a) > 0 after its original initiation at t = 0. Specifically, we consider the aged versions of the ensemble mean squared displacement (MSD) and the time averaged MSD (TAMSD). The aging subordinated FBM exhibits a disparity between MSD and TAMSD and is thus weakly nonergodic, while strong aging is shown to effect a convergence of the MSD and TAMSD. At long times, the MSD in the harmonic potential has a stationary value, that depends on the Hurst index of the parental (non-equilibrium) FBM. The TAMSD of confined subordinated FBM does not relax to a stationary value but increases sublinearly with lag time, analogously to confined CTRW. Interestingly, for the confined subordinated FBM, small aging time t(a) has no effect on the aged MSD, while at large aging time the aged MSD has monotonic increase ultimately with a power-law and is identical to the aged TAMSD. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)