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Cumulant approach of arbitrary truncated Levy flight

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  • Vinogradov, Dmitry V.

Abstract

The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved. The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found. The influence of truncation shape on the truncated Levy flight properties in the Gaussian and the Levy regimes has been investigated.

Suggested Citation

  • Vinogradov, Dmitry V., 2010. "Cumulant approach of arbitrary truncated Levy flight," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5794-5800.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:24:p:5794-5800
    DOI: 10.1016/j.physa.2010.09.014
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    References listed on IDEAS

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    1. 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.
    2. Grothe, Oliver & Schmidt, Rafael, 2010. "Scaling of Lévy–Student processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1455-1463.
    3. Gupta, Hari M. & Campanha, José R., 2000. "The gradually truncated Lévy flight: stochastic process for complex systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 275(3), pages 531-543.
    4. Srokowski, Tomasz, 2009. "Stretched-Gaussian asymptotics of the truncated Lévy flights for the diffusion in nonhomogeneous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1057-1066.
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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. Dmitry V. Vinogradov, 2012. "Arbitrary Truncated Levy Flight: Asymmetrical Truncation and High-Order Correlations," Papers 1205.3671, arXiv.org.
    3. Vinogradov, Dmitry V., 2012. "Arbitrary truncated Levy flight: Asymmetrical truncation and high-order correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5584-5597.

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