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Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy |
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| Authors: | L. Zunino,D.G. Pé rez,M.T. Martí n,M. Garavaglia,A. Plastino,O.A. Rosso |
| Affiliation: | a Centro de Investigaciones Ópticas, C.C. 124 Correo Central, 1900 La Plata, Argentina b Departamento de Ciencias Básicas, Facultad de Ingeniería, Universidad Nacional de La Plata (UNLP), 1900 La Plata, Argentina c Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, 1900 La Plata, Argentina d Instituto de Física, Pontificia Universidad Católica de Valparaíso (PUCV), 23-40025 Valparaíso, Chile e Instituto de Física (IFLP-CCT), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina f Buenos Aires Scientific Research Commission (CIC), C.C. 727, 1900 La Plata, Argentina g Argentina’s National Council (CCT-CONICET), C.C. 727, 1900 La Plata, Argentina h Centre for Bioinformatics, Biomarker Discovery and Information-Based Medicine, School of Electrical Engineering and Computer Science, The University of Newcastle, University Drive, Callaghan NSW 2308, Australia i Chaos & Biology Group, Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón II, Ciudad Universitaria, 1428 Ciudad de Buenos Aires, Argentina |
| Abstract: | In this work, we analyze two important stochastic processes, the fractional Brownian motion and fractional Gaussian noise, within the framework of the Tsallis permutation entropy. This entropic measure, evaluated after using the Bandt & Pompe method to extract the associated probability distribution, is shown to be a powerful tool to characterize fractal stochastic processes. It allows for a better discrimination of the processes than the Shannon counterpart for appropriate ranges of values of the entropic index. Moreover, we find the optimum value of this entropic index for the stochastic processes under study. |
| Keywords: | 02.50.-r 02.50.Ey 05.45.Tp 89.70.Cf |
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