It's clear that choosing large T and Δ Δ ≪ ≪ T can improve statistical performance. This technique allow us estimate the behavior of the whole ensembles by just measuring a single trajectory, but note that it's only valid for the systems with ergodicity, like classical Brownian motion (BM), fractional Brownian motion (fBM), and continuous-time random walk (CTRW) with limited distribution of waiting times, in these cases, δ δ 2 ( Δ Δ ) ¯ ¯ = ⟨ [ r ( t ) − − r ( 0 ) ] 2 ⟩ (defined above), here ⟨ ⋅ ⋅ ⟩ denotes ensembles average. However, for non-ergodic systems, like the CTRW with unlimited waiting time, waiting time can go to infinity at some time, in this case, δ δ 2 ( Δ Δ ) ¯ ¯ strongly depends on T , δ δ 2 ( Δ Δ ) ¯ ¯ and ⟨ [ r ( t ) − − r ( 0 ) ] 2 ⟩ don't equal each other anymore, in order to get better asymptotics, introduce the averaged time MSD :