Scaled Brownian motion as a mean-field model for continuous-time random walks

Felix Thiel, Igor M. Sokolov

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87 Scopus citations


We consider scaled Brownian motion (sBm), a random process described by a diffusion equation with explicitly time-dependent diffusion coefficient D(t)=αD0tα-1 (Batchelor's equation) which, for α<1, is often used for fitting experimental data for subdiffusion of unclear genesis. We show that this process is a close relative of subdiffusive continuous-time random walks and describes the motion of the rescaled mean position of a cloud of independent walkers. It shares with subdiffusive continuous-time random walks its nonstationary and nonergodic properties. The nonergodicity of sBm does not however go hand in hand with strong difference between its different realizations: its heterogeneity ("ergodicity breaking") parameter tends to zero for long trajectories.

Original languageEnglish
Article number012115
JournalPhysical Review E
Issue number1
StatePublished - 13 Jan 2014
Externally publishedYes


FundersFunder number
Deutsche Forschungsgemeinschaft


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