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Transient superdiffusion in random walks with a q-exponentially decaying memory profile

Author

Listed:
  • Moura, Thiago R.S.
  • Viswanathan, G.M.
  • da Silva, M.A.A.
  • Cressoni, J.C.
  • da Silva, L.R.

Abstract

We propose a random walk model with q-exponentially decaying memory profile. The q-exponential function is a generalization of the ordinary exponential function. In the limit q→1, the q-exponential becomes the ordinary exponential function. This model presents a Markovian diffusive regime that is characterized by finite memory correlations. It is well known, that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. In this problem we report the outcome of a transient superdiffusion for finite sized walks.

Suggested Citation

  • Moura, Thiago R.S. & Viswanathan, G.M. & da Silva, M.A.A. & Cressoni, J.C. & da Silva, L.R., 2016. "Transient superdiffusion in random walks with a q-exponentially decaying memory profile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 259-263.
    • Handle: RePEc:eee:phsmap:v:453:y:2016:i:c:p:259-263
    DOI: 10.1016/j.physa.2016.02.005
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    References listed on IDEAS

    as
    1. Serletis, Apostolos & Rosenberg, Aryeh Adam, 2007. "The Hurst exponent in energy futures prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 325-332.
    2. M. L. Felisberto & F. S. Passos & A. S. Ferreira & M. A.A. da Silva & J. C. Cressoni & G. M. Viswanathan, 2009. "Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(3), pages 427-433, December.
    3. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
    4. repec:clg:wpaper:2007-02 is not listed on IDEAS
    5. da Silva, M.A.A. & Cressoni, J.C. & Viswanathan, G.M., 2006. "Discrete-time non-Markovian random walks: The effect of memory limitations on scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 70-78.
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    Cited by:

    1. Gut, Allan & Stadtmüller, Ulrich, 2022. "The elephant random walk with gradually increasing memory," Statistics & Probability Letters, Elsevier, vol. 189(C).
    2. de Lacerda, K.J.C.C. & da Silva, L.R. & Viswanathan, G.M. & Cressoni, J.C. & da Silva, M.A.A., 2022. "A random walk model with a mixed memory profile: Exponential and rectangular profile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).

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