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

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