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Lévy models and scale invariance properties applied to Geophysics

Author

Listed:
  • Mariani, M.C.
  • Florescu, I.
  • SenGupta, I.
  • Beccar Varela, M.P.
  • Bezdek, P.
  • Serpa, L.

Abstract

In this work we study scale invariant functions and stochastic Lévy models and we apply them to geophysical data. We show that a pattern arises from the scale invariance property and Lévy flight models that may be used to estimate parameters related to some major event–major earthquakes.

Suggested Citation

  • Mariani, M.C. & Florescu, I. & SenGupta, I. & Beccar Varela, M.P. & Bezdek, P. & Serpa, L., 2013. "Lévy models and scale invariance properties applied to Geophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 824-839.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:4:p:824-839
    DOI: 10.1016/j.physa.2012.11.007
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    2. Mariani, Maria Cristina & Liu, Yang, 2006. "A new analysis of intermittence, scale invariance and characteristic scales applied to the behavior of financial indices near a crash," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 345-352.
    3. E. Barany & M. P. Beccar Varela & I. Florescu & I. Sengupta, 2012. "Detecting market crashes by analysing long-memory effects using high-frequency data," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 623-634, April.
    4. Sornette, Didier & Johansen, Anders, 1997. "Large financial crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 411-422.
    5. Mariani, M.C. & Liu, Y., 2007. "Normalized truncated Levy walks applied to the study of financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 590-598.
    6. Anders Johansen & Olivier Ledoit & Didier Sornette, 2000. "Crashes As Critical Points," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 219-255.
    7. Mariani, M.C. & Liu, Y., 2007. "A new analysis of the effects of the Asian crisis of 1997 on emergent markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 307-316.
    8. Mariani, M.C. & Libbin, J.D. & Kumar Mani, V. & Beccar Varela, M.P. & Erickson, C.A. & Valles-Rosales, D.J., 2008. "Long correlations and Normalized Truncated Levy Models applied to the study of Indian Market Indices in comparison with other emerging markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1273-1282.
    9. Ferraro, Marta & Furman, Nicolas & Liu, Yang & Mariani, Cristina & Rial, Diego, 2006. "Analysis of intermittence, scale invariance and characteristic scales in the behavior of major indices near a crash," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 576-588.
    10. Mariani, M.C. & Bezdek, P. & Serpa, L. & Florescu, I., 2011. "Ising type models applied to Geophysics and high frequency market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4396-4402.
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    Cited by:

    1. Kanadpriya Basu & Maria C. Mariani & Laura Serpa & Ritwik Sinha, 2015. "Evaluation of Interpolants in Their Ability to Fit Seismometric Time Series," Mathematics, MDPI, vol. 3(3), pages 1-24, August.
    2. Mariani, Maria C. & Tweneboah, Osei K., 2016. "Stochastic differential equations applied to the study of geophysical and financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 170-178.
    3. Beccar-Varela, Maria P. & Mariani, Maria C. & Tweneboah, Osei K. & Florescu, Ionut, 2017. "Analysis of the Lehman Brothers collapse and the Flash Crash event by applying wavelets methodologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 162-171.
    4. Beccar-Varela, Maria P. & Gonzalez-Huizar, Hector & Mariani, Maria C. & Tweneboah, Osei K., 2016. "Use of wavelets techniques to discriminate between explosions and natural earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 42-51.
    5. Mariani, Maria C. & Basu, Kanadpriya, 2015. "Spline interpolation techniques applied to the study of geophysical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 68-79.
    6. Habtemicael, Semere & SenGupta, Indranil, 2014. "Ornstein–Uhlenbeck processes for geophysical data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 147-156.

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