Figure 1

(Color online) Panels (a) and (b) present $V_n^{\left(1/H\right)}\left(t\right)$ and $V_n^{\left(2\right)}\left(t\right)$, respectively, corresponding to the CTRW process $Z_{\alpha }\left(t\right)$. In panels (c) and (d) we see $V_n^{\left(1/H\right)}\left(t\right)$ and $V_n^{\left(2\right)}\left(t\right)$, respectively, corresponding to the process $Y_H\left(t\right)$. The potential here is harmonic $v\left(x\right)=x^2/2$. The parameters are $\alpha =0.8,H=\alpha /2=0.4,\sigma =1,K=1/2$. See Sec. 3 for the detailed discussion of the results.Reuse & Permissions

Figure 2

(Color online) Panel (a) shows the experimental trajectory (Golding-Cox data), panels (b) and (c) depict the corresponding sums $V_n^{\left(1/H\right)}\left(t\right)$ and $V_n^{\left(2\right)}\left(t\right)$, respectively. In panels (d)-(f) we see analogous graphs corresponding to the simulated trajectory of $Y_H\left(t\right)$. Panels (g)-(i) depict the results corresponding to the simulated trajectory of $Z_{\alpha }\left(t\right)$. The parameters used in simulations were estimated from the experimental trajectory. Here, $H=\alpha /2=0.35$ (as in [2]), upper and lower reflecting boundaries are placed at 0.19 and $-0.47$, respectively, the standard deviation of the increments of all processes equals 0.03. In all the panels with the sums $V_n^{\left(1/H\right)}\left(t\right)$ and $V_n^{\left(2\right)}\left(t\right)$ we used the following notation: $n=10$ (blue line); $n=9$ (red line); $n=8$ (green line); $n=7$ (black line). The dotted line in panels (b) and (e) is the theoretical value of $V^{\left(1/H\right)}\left(t\right)$ corresponding to $Y_H\left(t\right)$ [see formula (8)]. See Sec. 3 for the detailed discussion of the results.Reuse & Permissions

Figure 3

(Color online) $P$ values calculated for the Golding-Cox empirical trajectories under the null hypothesis: (a) that the data comes from FBM; (b) that the data comes from CTRW. See Sec. 4 for the detailed discussion of the results.Reuse & Permissions