Fig. 1

Different correlation characteristics of two random processes. The upper subplots are two typical samples from the first-order Gauss–Markov process \({\dot{\alpha }}(t) = -\frac{1}{T}\alpha (t) + w(t)\), with \(w(t)\sim N(0, 2 \sigma ^2/T )\), where x and y have the same parameter \(\sigma\) but different correlation times T; the lower two are defined as \(\Delta \alpha (t) = \alpha (t) - \alpha (t+\Delta t)\)