IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v81y2011i1p146-152.html
   My bibliography  Save this article

Fractional normal inverse Gaussian diffusion

Author

Listed:
  • Kumar, A.
  • Meerschaert, Mark M.
  • Vellaisamy, P.

Abstract

A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated to an inverse Gaussian process. This paper shows how the FNIG process emerges naturally as the limit of a random walk with correlated jumps separated by i.i.d. waiting times. Similarly, we show that the NIG process, a Brownian motion subordinated to an inverse Gaussian process, is the limit of a random walk with uncorrelated jumps separated by i.i.d. waiting times. The FNIG process is also derived as the limit of a fractional ARIMA processes. Finally, the NIG densities are shown to solve the relativistic diffusion equation from statistical physics.

Suggested Citation

  • Kumar, A. & Meerschaert, Mark M. & Vellaisamy, P., 2011. "Fractional normal inverse Gaussian diffusion," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 146-152, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:146-152
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00283-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2009. "Correlated continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1194-1202, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    2. Gajda, J. & Kumar, A. & Wyłomańska, A., 2019. "Stable Lévy process delayed by tempered stable subordinator," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 284-292.
    3. Kumar, A. & Nane, Erkan & Vellaisamy, P., 2011. "Time-changed Poisson processes," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1899-1910.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Meerschaert, Mark M. & Nane, Erkan & Xiao, Yimin, 2013. "Fractal dimension results for continuous time random walks," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1083-1093.
    2. Chen, Zhenlong & Xu, Lin & Zhu, Dongjin, 2015. "Generalized continuous time random walks and Hermite processes," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 44-53.
    3. Nane, Erkan, 2009. "Laws of the iterated logarithm for a class of iterated processes," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1744-1751, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:146-152. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.