38596
2015
2015
eng
18
37
48
article
IOP Publ. Ltd.
Bristol
1
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Quantifying the non-ergodicity of scaled Brownian motion
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.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/48/37/375002
1751-8113 (print)
1751-8121 (online)
wos:2015
375002
WOS:000361551700004
Safdari, H (reprint author), Shahid Beheshti Univ, Dept Phys, GC, Tehran 19839, Iran., rmetzler@uni-potsdam.de
Academy of Finland (Suomen Akatemia, Finland Distinguished
Professorship); Deutsche Forschungsgemeinschaft; IMU Berlin Einstein
Foundation
Hadiseh Safdari
Andrey G. Cherstvy
Aleksei V. Chechkin
Felix Thiel
Igor M. Sokolov
Ralf Metzler
eng
uncontrolled
scaled Brownian motion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
ageing
Institut für Physik und Astronomie
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