Fractional brownian motion versus the continuous-time random walk: a simple test for subdiffusive dynamics.

@article{Magdziarz2009FractionalBM,
  title={Fractional brownian motion versus the continuous-time random walk: a simple test for subdiffusive dynamics.},
  author={Marcin Magdziarz and Aleksander Weron and Krzysztof Burnecki and Joseph Klafter},
  journal={Physical review letters},
  year={2009},
  volume={103 18},
  pages={180602}
}
Fractional Brownian motion with Hurst index less then 1/2 and continuous-time random walk with heavy tailed waiting times (and the corresponding fractional Fokker-Planck equation) are two different processes that lead to a subdiffusive behavior widespread in complex systems. We propose a simple test, based on the analysis of the so-called p variations, which allows distinguishing between the two models on the basis of one realization of the unknown process. We apply the test to the data of… CONTINUE READING

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