Refined scaling hypothesis for anomalously diffusing processes

R. Badii and P. Talkner

Physica A: Statistical Mechanics and its Applications, 2001, vol. 291, issue 1, 229-243

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.

Keywords: Scaling; Anomalous diffusion; Stochastic self-affinity; Fractional Brownian motion; Turbulence; EEG; Economics (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:291:y:2001:i:1:p:229-243

DOI: 10.1016/S0378-4371(00)00494-5

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