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Refined scaling hypothesis for anomalously diffusing processes

Author

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  • Badii, R.
  • Talkner, P.

Abstract

Anomalous diffusion in artificial and natural stochastic processes is studied through the statistics of small-scale fluctuations. It is shown that the moments of certain locally averaged quantities, such as the square or absolute increments, do not scale like power laws, as generally assumed. A much improved scaling function is deduced, in analogy with a procedure first applied to nearest-neighbour dimension estimators. Extremely accurate determination of the scaling exponents is thus possible. Our refined formula is immediately applicable to the analysis of time series in turbulence, physiology, or economics.

Suggested Citation

  • Badii, R. & Talkner, P., 2001. "Refined scaling hypothesis for anomalously diffusing processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 229-243.
    • Handle: RePEc:eee:phsmap:v:291:y:2001:i:1:p:229-243
    DOI: 10.1016/S0378-4371(00)00494-5
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