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First hitting time models for the generalized inverse Gaussian distribution

Author

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  • Barndorff-Nielsen, O.
  • Blæsild, P.
  • Halgreen, C.

Abstract

Any generalized inverse Gaussian distribution with a non-positive power parameter is shown to be the distribution of the first hitting time of level 0 for each of a variety of time-homogeneous diffusions on the interval [0, [infinity]). The infinite divisibility of the generalized inverse Gaussian distributions is a simple consequence of this and an elementary convolution formula for these distributions.

Suggested Citation

  • Barndorff-Nielsen, O. & Blæsild, P. & Halgreen, C., 1978. "First hitting time models for the generalized inverse Gaussian distribution," Stochastic Processes and their Applications, Elsevier, vol. 7(1), pages 49-54, March.
    • Handle: RePEc:eee:spapps:v:7:y:1978:i:1:p:49-54
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    Cited by:

    1. Hariya, Yuu, 2020. "On some identities in law involving exponential functionals of Brownian motion and Cauchy random variable," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 5999-6037.
    2. Lemonte, Artur J. & Cordeiro, Gauss M., 2011. "The exponentiated generalized inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 506-517, April.
    3. Matsumoto, Hiroyuki & Yor, Marc, 2003. "Interpretation via Brownian motion of some independence properties between GIG and gamma variables," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 253-259, February.
    4. Thabane, Lehana & Drekic, Steve, 2003. "Hypothesis testing for the generalized multivariate modified Bessel model," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 360-374, August.
    5. Jedidi, Wissem & Simon, Thomas, 2015. "Diffusion hitting times and the bell-shape," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 38-41.
    6. Eduardo A Aponte & Dario Schöbi & Klaas E Stephan & Jakob Heinzle, 2017. "The Stochastic Early Reaction, Inhibition, and late Action (SERIA) model for antisaccades," PLOS Computational Biology, Public Library of Science, vol. 13(8), pages 1-36, August.

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