Figure 1
From: Quantifying non-ergodicity of anomalous diffusion with higher order moments
EB parameter of FBM divided by the respective scaling laws with respect to Δ/t for the regimes 0 < α < 3/2 and 3/2 < α < 2 according to Eq. (10). The behaviour according to Eq. (10) from45 is represented by the dashed red lines and the red symbol at α = 3/2: it shows a distinct divergence at α = 3/2. Our analytical result (12) based on a less severe approximation is represented by the symbols and the full line corresponding to the numerical evaluation of the integral (11), calculated via the trapezoidal rule with integration step 10−3. No divergence remains, and in fact a continuous albeit non-smooth behaviour is revealed. The agreement between our approximation (12) and the numerical evaluation of the full expression (11) remains quite good even for relatively large values of Δ/t. Note the left and right ordinates referring to the cases 0 < α < 3/2 and 3/2 < α < 2.
