GENERALIZED(m, k)-ZipfLAW FOR FRACTIONAL BROWNIAN MOTION-LIKE TIME SERIES WITH OR WITHOUT EFFECT OF AN ADDITIONAL LINEAR TREND

Ph. Bronlet and Marcel Ausloos
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Ph. Bronlet: SUPRAS and GRASP, B5, Sart Tilman Campus, B-4000 Liège, Euroland

International Journal of Modern Physics C (IJMPC), 2003, vol. 14, issue 03, 351-365

Abstract: We have translated fractional Brownian motion (FBM) signals into a text based on two "letters", as if the signal fluctuations correspond to a constant stepsize random walk. We have applied the Zipf method to extract the ζ′ exponent relating the word frequency and its rank on a log–log plot. We have studied the variation of the Zipf exponent(s) giving the relationship between the frequency of occurrence of words of lengthm

Keywords: Zipf; fractional Brownian motion; Hurst exponent; trend (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1142/S0129183103004528

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