Anomalous diffusion as a stochastic component in the dynamics of complex processes

We propose an interpolation expression using the difference moment (Kolmogorov transient structural function) of the second order as the average characteristic of displacements for identifying the anomalous diffusion in complex processes when the stochastic (the term "stochastic" in this paper refers to random variability in the signals of complex systems characterized by nonlinear interactions, dissipation, and inertia) dynamics of the system under study reaches a steady state (large time intervals). Our procedure based on this expression for identifying anomalous diffusion and calculating its parameters in complex processes is applied to the analysis of the dynamics of blinking fluorescence of quantum dots, x-ray emission from accreting objects, fluid velocity in Rayleigh-Bénard convection, and geoelectrical signal for a seismic area. For all four examples, the proposed interpolation is able to adequately describe the stochastic part of the experimental difference moment, which implies that anomalous diffusion manifests itself in these complex processes. The results of this study make it possible to broaden the range of complex natural processes in which anomalous diffusion can be identified.