TY - JOUR
A1 - Safdari, Hadiseh
A1 - Cherstvy, Andrey G.
A1 - Chechkin, Aleksei V.
A1 - Thiel, Felix
A1 - Sokolov, Igor M.
A1 - Metzler, Ralf
T1 - Quantifying the non-ergodicity of scaled Brownian motion
JF - Journal of physics : A, Mathematical and theoretical
N2 - We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form D(t) similar or equal to t(alpha-1). We compute the ergodicity breaking parameter EB in the entire range of scaling exponents a, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Delta the EB parameter as function of the scaling exponent a has no divergence at alpha - 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.
KW - scaled Brownian motion
KW - anomalous diffusion
KW - ageing
Y1 - 2015
U6 - http://dx.doi.org/10.1088/1751-8113/48/37/375002
SN - 1751-8113 (print)
SN - 1751-8121 (online)
VL - 48
IS - 37
PB - IOP Publ. Ltd.
CY - Bristol
ER -