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Original Articles

Characterization of discrete scale invariant Markov sequences

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Pages 5263-5278 | Received 07 Apr 2013, Accepted 01 Jul 2014, Published online: 11 Jul 2016

References

  • Balasis, G., Papadimitriou, C., Daglis, I.A., Anastasiadis, A., Athanasopoulou, L., Eftaxias, K. (2011a). Signatures of discrete scale invariance in Dst time series. Geophys. Res. Lett. 38:L13103. doi:10.1029/2011GL048019.
  • Balasis, G., Daglis, I.A., Anastasiadis, A., Athanasopoulou, L., Eftaxias, K. (2011b). Detection of dynamical complexity changes in Dst time series using entropy concepts and rescaled range analysis. In Liu, W., Fujimoto, M., eds., The Dynamic Magnetosphere, IAGA Special Sopron Book Series (Vol. 3, part 3, pp. 211–220). Springer. doi:10.1007/978-94-007-0501-2-12.
  • Bartolozzi, M., Drozdz, S., Leieber, D.B., Speth, J., Thomas, A.W. (2005). Self-similar log-periodic structures in western stock markets from 2000. Int. J. Mod. Phys. C 16(9):1347–1361.
  • Borgnat, P., Amblard, P.O., Flandrin, P. (2005). Scale invariances and Lamperti transformations for stochastic processes. J. Phys. A: Math. Gener. 38:2081–2101.
  • Borgnat, P., Flandrin, P., Amblard, P.O. (2002). Stochastic discrete scale invariance. IEEE Signal Process. Lett. 9:181–184.
  • Borisov, I.S. (1982). On a criterion for Gaussian random processes to be Markovian. Theory Probab. Appl. 27:863–865.
  • Burnecki, K., Maejima, M., Weron, A. (1997). The Lamperti transformation for self-similar processes. Yokohama Math. J. 44:25–42.
  • Doob, J.L. (1953). Stochastic Processes. New York, NY: Wiley.
  • Gray, H.L., Zhang, N.F. (1988). On a class of nonstationary processes. J. Time Ser. Anal. 9(2):133–154.
  • Hurst, H.E. (1951). Long-term storage of reservoirs: an experimental study. Trans. Am. Soc. Civ. Eng. 116:770–799.
  • Modarresi, N., Rezakhah, S. (2010). Spectral analysis of Multi-dimensional self-similar Markov processes. J. Phys. A: Math. Theor. 43(12):125004 (14pp).
  • Modarresi, N., Rezakhah, S. (2013). A new structure for analyzing discrete scale invariant processes: covariance and spectra. J. Stat. Phys. 152(6):15pp. doi:10.1007/s10955-013-0799-4.
  • Nuzman, C.J., Poor, H.V. (2000). Linear estimation of self-similar processes via Lamperti’s transformation. J. Appl. Probab. 37(2):429–452.
  • Rezakhah, S., Philippe, A., Modarresi, N. (2013). Estimation of Scale and Hurst Parameters of Semi-Selfsimilar Processes. Available at: http://arxiv.org/pdf/1207.2450v1.pdf.
  • Shao, Q., Lund, R.B. (2004). Computation and characterization of autocorrelations and partial autocorrelations in periodic ARMA models. J. Time Ser. Anal. 25(3):359–372.
  • Shishebor, Z., Nematollahi, A.R., Soltani, A.R. (2006). On covariance generating functions and spectral densities of periodically correlated autoregressive processes. J. Appl. Math. Stochastic Anal. 2006:1–17.
  • Sornette, D. (1998). Discrete scale invariance and complex dimensions. Phys. Rep. 297:239–270.
  • Vidacs, A., Virtamo, J. (1999). ML estimation of the parameters of fBm traffic with geometrical sampling. IFIP TC6, Int. Conf. on Broadband communications 99, November 10–12, 1999, Hong-Kong.
  • Zhou, W.X., Sornette, D. (2009). Numerical investigations of discrete scale invariance in fractals and multifractal measures. Physica A 388(13):2623–2639.

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