Automatic algorithm to decompose discrete paths of fractional Brownian motion into self-similar intrinsic components

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• 作者：C?lin Vamo? ; Maria Cr?ciun ; Nicolae Suciu
• 关键词：Computational Methods
• 刊名：The European Physical Journal B - Condensed Matter
• 出版年：2015
• 出版时间：October 2015
• 年：2015
• 卷：88
• 期：10
• 全文大小：535 KB
• 参考文献：1. J. Gao, Y. Cao, W. Tung, J. Hu, Multiscale Analysis of Complex Time Series (Wiley, Hoboken, 2007)
  2.D.B. Percival, A.T. Walden, Wavelet Methods for Time Series Analysis (Cambridge University Press, Cambridge, 2000)
  3. N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung, H.H. Liu, Proc. R. Soc. Lond. A 454, 903 (1998) MathSciNet CrossRef ADS MATH
  4. L. Lin, Y. Wang, H. Zhou, Adv. Adapt. Data Anal. 1, 543 (2009)MathSciNet CrossRef
  5. I. Daubechies, J. Lu, H.-T. Wu, Appl. Comput. Harmon. Anal. 30, 243 (2011)MathSciNet CrossRef MATH
  6. T.Y. Hou, Z. Shi, Adv. Adapt. Data Anal. 3, 1 (2011)MathSciNet CrossRef MATH
  7. B. Boashash, Proc. IEEE 80, 520 (1992)CrossRef ADS
  8. C. Vamo?, M. Cr?ciun, Eur. Phys. J. B 87, 301 (2014)CrossRef ADS
  9. B.B. Mandelbrot, J.W. Van Ness, SIAM Rev. 10, 422 (1968)MathSciNet CrossRef ADS MATH
  10. A. Carbone, G. Castelli, H.E. Stanley, Phys. Rev. E 69, 026105 (2004) CrossRef ADS
  11. A. Carbone, Phys. Rev. E 76, 056703 (2007) MathSciNet CrossRef ADS
  12. B.B. Mandelbrot, J.R. Wallis Noah, Water Resour. Res. 4, 909 (1968)CrossRef ADS
  13.T. Graves, R.B. Gramscy, N.Watkins, C.L.E. Franzke, arXiv:1406.6018 [stat.OT] (2014)
  14. N. Suciu, Phys. Rev. E 81, 056301 (2010) CrossRef ADS
  15.A.N. Shiryaev, Essentials of Stochastic Finance. Facts, Models, Theory (World Scientific, Singapore, 1999)
  16.R. Cont, in Proceedings of the Fractals in Engineering, edited by J. Lévy Véhel, E. Lutton (Springer, London, 2005), p. 159
  17. W.E. Leland, M.S. Taqqu, W. Willinger, D.V. Wilson, IEEE/ACM Trans. Networking 2, 1 (1994)CrossRef
  18. S. Stoev, M.S. Taqqu, C. Park, J.S. Marron, Computer Networking 48, 423 (2005)CrossRef
  19.D.L. Turcotte, Fractals and Chaos in Geology and Geophysics, 2nd edn. (Cambridge University Press, Cambridge, 1997)
  20.P.S. Addison, Fractals and Chaos. An Illustrated Course, (Institute of Physics Publishing, London, 1997)
  21. M.G. Trefry, F.P. Ruan, D. McLaughlin, Water Resour. Res. 39, 1063 (2003) ADS
  22. A. Fiori, I. Jankovic, G. Dagan, Water Resour. Res. 42, W06D13 (2006)
  23. C. Vamo?, M. Cr?ciun, Phys. Rev. E 78, 036707 (2008) CrossRef ADS
  24. C. Vamo?, M. Cr?ciun, Automatic Trend Estimation (Springer, Dordrecht, 2012)
  25.J.-M. Bardet, G. Lang, G. Oppenheim, A. Philippe, S. Stoev, M.S. Taqqu, in Theory and applications of long-range dependence, edited by P. Doukhan, G. Oppenheim, M. Taqqu, (Birkh?user, Boston, 2003), p. 579
  26. Y. Meyer, F. Sellan, M.S. Taqqu, J. Fourier Anal. Appl. 5, 465 (2000)MathSciNet CrossRef
  27. P. Abry, F. Sellan, Appl. Comp. Harmonic Anal., 3, 377 (1996) MathSciNet CrossRef MATH
  28. N. Suciu, Adv. Water Resour. 69, 114 (2014)CrossRef ADS
  29. H. Schwarze, U. Jaekel, H. Vereecken, Transport Porous Med. 43, 265 (2001)CrossRef
  30. R.H. Kraichnan, Phys. Fluids 13, 22 (1970)CrossRef ADS MATH
  31. J. Eberhard, N. Suciu, C. Vamos, J. Phys. A 40, 597 (2007)MathSciNet CrossRef ADS MATH
  32. N. Suciu, S. Attinger, F.A. Radu, C. Vamo?, J. Vanderborght, H. Vereecken, P. Knabner, An. St. Univ. Ovidius Constanta 23, 167 (2015)
  33. Y. Huang, F.G. Schmitt, J.-P. Hermand, Y. Gagne, Z. Lu, Y. Liu, Phys. Rev. E 84, 016208 (2011) CrossRef ADS
  34.L. Calvet, A. Fisher, B. Mandelbrot, Large deviations and the distribution of price changes (Cowles Foundation Discussion Paper, 1997)
  
• 作者单位：C?lin Vamo? (1)
  Maria Cr?ciun (1)
  Nicolae Suciu (1) (2)
  
  1. T. Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68, 400110, Cluj-Napoca, Romania
  2. Mathematics Department, Friedrich Alexander University of Erlangen-Nuremberg, Cauerstra?e 11, 91058, Erlangen, Germany
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Condensed Matter
  Physics
  Complexity
  Fluids
  Solid State Physics and Spectroscopy
  Superconductivity, Superfluidity and Quantum Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1434-6036

文摘

Fractional Brownian motion (fBm) is a nonstationary self-similar continuous stochastic process used to model many natural phenomena. A realization of the fBm can be numerically approximated by discrete paths which do not entirely preserve the self-similarity. We investigate the self-similarity at different time scales by decomposing the discrete paths of fBm into intrinsic components. The decomposition is realized by an automatic numerical algorithm based on successive smoothings stopped when the maximum monotonic variation of the averaged time series is reached. The spectral properties of the intrinsic components are analyzed through the monotony spectrum defined as the graph of the amplitudes of the monotonic segments with respect to their lengths (characteristic times). We show that, at intermediate time scales, the mean amplitude of the intrinsic components of discrete fBms scales with the mean characteristic time as a power law identical to that of the corresponding continuous fBm. As an application we consider hydrological time series of the transverse component of the transport process generated as a superposition of diffusive movements on advective transport in random velocity fields. We found that the transverse component has a rich structure of scales, which is not revealed by the analysis of the global variance, and that its intrinsic components may be self-similar only in particular cases. Keywords Computational Methods