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Fractional Normal Inverse Gaussian Process

Author

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  • Arun Kumar

    (Indian Institute of Technology Bombay)

  • Palaniappan Vellaisamy

    (Indian Institute of Technology Bombay)

Abstract

Normal inverse Gaussian (NIG) process was introduced by Barndorff-Nielsen (Scand J Statist 24:1–13, 1997) by subordinating Brownian motion with drift to an inverse Gaussian process. Increments of NIG process are independent and are stationary. In this paper, we introduce dependence between the increments of NIG process, by subordinating fractional Brownian motion to an inverse Gaussian process and call it fractional normal inverse Gaussian (FNIG) process. The basic properties of this process are discussed. Its marginal distributions are scale mixtures of normal laws, infinitely divisible for the Hurst parameter 1/2 ≤ H

Suggested Citation

  • Arun Kumar & Palaniappan Vellaisamy, 2012. "Fractional Normal Inverse Gaussian Process," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 263-283, June.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:2:d:10.1007_s11009-010-9201-z
    DOI: 10.1007/s11009-010-9201-z
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    References listed on IDEAS

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    Cited by:

    1. Sung Ik Kim, 2022. "ARMA–GARCH model with fractional generalized hyperbolic innovations," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-25, December.

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