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The gradually truncated Lévy flight for systems with power-law distributions

Author

Listed:
  • Gupta, Hari M.
  • Campanha, José R.

Abstract

Power-law distributions have been observed in various economical and physical systems. Lévy flights have infinite variance which discourage a physical approach. We introduce a class of stochastic processes, the “gradually truncated Lévy flight” in which large steps of a Lévy flight are gradually eliminated. It has finite variance and the system can be analyzed in a closed form. We applied the present method to explain the distribution of a particular economical index. The present method can be applied to describe time series in a variety of fields, i.e. turbulent flow, anomalous diffusion, polymers, etc.

Suggested Citation

  • Gupta, Hari M. & Campanha, José R., 1999. "The gradually truncated Lévy flight for systems with power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 231-239.
    • Handle: RePEc:eee:phsmap:v:268:y:1999:i:1:p:231-239
    DOI: 10.1016/S0378-4371(99)00028-X
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    Citations

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    Cited by:

    1. Imai, Junichi & Kawai, Reiichiro, 2011. "On finite truncation of infinite shot noise series representation of tempered stable laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4411-4425.
    2. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    3. Matsushita, Raul & Gleria, Iram & Figueiredo, Annibal & Rathie, Pushpa & Da Silva, Sergio, 2004. "Exponentially damped Lévy flights, multiscaling, and exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 353-369.
    4. Liu, Lei & Hu, Fei, 2013. "Cascade-like and scaling behavior of wind velocity increments in the atmospheric surface layer," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5808-5816.
    5. Gleria, Iram & Figueiredo, Annibal & Matsushita, Raul & Rathie, Pushpa & Da Silva, Sergio, 2004. "Exponentially damped Lévy flights, multiscaling and slow convergence in stockmarkets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 200-206.
    6. Matsushita, Raul & Rathie, Pushpa & Da Silva, Sergio, 2003. "Exponentially damped Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 326(3), pages 544-555.
    7. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.
    8. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    9. Matsushita, Raul & Da Silva, Sergio & Da Fonseca, Regina & Nagata, Mateus, 2020. "Bypassing the truncation problem of truncated Lévy flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    10. Dorea, Chang C.Y. & Guevara Otiniano, Cira E. & Matsushita, Raul & Rathie, Pushpa N., 2007. "Levy flight approximations for scaled transformations of random walks," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6343-6354, August.
    11. Sergio Da Silva, 2004. "International Finance, Levy Distributions, and the Econophysics of Exchange Rates," International Finance 0405018, University Library of Munich, Germany.
    12. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    13. Schinckus, C., 2013. "Between complexity of modelling and modelling of complexity: An essay on econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3654-3665.

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