Source code and datasets for the paper "Super-diffusion in stochastic processes with long-range memory"

The repository accompanies the manuscript "Super-diffusion in stochastic processes with long-range memory", published in Physical Review E (https://doi.org/10.1103/j7d9-zlh9). The program performs numerical simulation of stochastic processes with long-range correlations using power-law memory functions and calculates their statistical characteristics. Files: MemProc.py - Python source code, containing the main class "ProcPow" for generating and analyzing the stochastic process samples with the given power-law memory function. To use it, uncomment one of two lines in the end of the file: ProcPow.calc_save_combined(...) - Generate a set of process samples, calculate the variance V(t), and save it to data files. The resulting folder contains the following files (examples of such datasets for different memory exponent can be found in the archive "DATA.rar"): "params.json" - JSON file of the generation parameters; "variance.txt" - the numerically calculated variance at the log time scale; "process.txt" - one random sample of the generated process. ProcPow.load_draw_combined() - Load a previously saved dataset, plot the process sample, the calculated response function h(t) and the variance V(t). "DATA.rar" - Examples of generated datasets for three cases of the memory exponent: β=2.1, β=2.4 and β=3.5. "beta_2.4.png" - Example of the resulting plots for the memory exponent β=2.4.