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Randomness and fractional stable distributions

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  • Tapiero, Charles S.
  • Vallois, Pierre

Abstract

Stochastic and fractional models are defined by applications of Liouville (and other) fractional operators. They underlie anomalous transport dynamical properties such as long range temporal correlations manifested in power laws. Prolific applications to finance and other domains have been published, based mostly on a randomness defined by the fractional Brownian Motion. Application to probability distributions (Tapiero and Vallois 2016, 2017, 2018), have indicated that fractional distributions are incomplete and their limit distributions (based on the Central LimitTheorem) depend on their fractional index. For example, for a fractional index 1∕2≤H≤1, we showed that a fractional Brownian Bridge defines a fractional randomness (rather than a Brownian Motion). In this paper we consider the case 0

Suggested Citation

  • Tapiero, Charles S. & Vallois, Pierre, 2018. "Randomness and fractional stable distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 54-60.
    • Handle: RePEc:eee:phsmap:v:511:y:2018:i:c:p:54-60
    DOI: 10.1016/j.physa.2018.07.019
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    References listed on IDEAS

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    1. Tapiero, Charles S. & Vallois, Pierre, 2018. "Fractional Randomness and the Brownian Bridge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 835-843.
    2. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
    3. Tapiero, Charles S. & Vallois, Pierre, 2016. "Fractional randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1161-1177.
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    Cited by:

    1. Gurjeet Dhesi & Bilal Shakeel & Marcel Ausloos, 2021. "Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach," Annals of Operations Research, Springer, vol. 299(1), pages 1397-1410, April.

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