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Interpretation via Brownian motion of some independence properties between GIG and gamma variables

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  • Matsumoto, Hiroyuki
  • Yor, Marc

Abstract

In the course of our investigations of exponential Brownian functionals (Nagoya Math. J. 162 (2001) 65) we noticed, with the help of some previous work by Letac and Seshadri (Z. Wahr. verw. Geb. 62 (1983) 485), some identity in law involving GIG and gamma variables. In the present note, we give a detailed and self-contained proof of this identity in law, which relies only on the exponential Brownian functionals framework.

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  • 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.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:3:p:253-259
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Bobecka, Konstancja, 2015. "The Matsumoto–Yor property on trees for matrix variates of different dimensions," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 22-34.
    2. Massam, Hélène & Wesolowski, Jacek, 2006. "The Matsumoto-Yor property and the structure of the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 103-123, January.
    3. Wesolowski, Jacek & Witkowski, Piotr, 2007. "Hitting times of Brownian motion and the Matsumoto-Yor property on trees," Stochastic Processes and their Applications, Elsevier, vol. 117(9), pages 1303-1315, September.
    4. Chou, Chao-Wei & Huang, Wen-Jang, 2004. "On characterizations of the gamma and generalized inverse Gaussian distributions," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 381-388, October.
    5. Hariya, Yuu & Yor, Marc, 2004. "On an extension of Dufresne's relation between exponential Brownian functionals from opposite drifts to two different drifts: a short proof," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 331-341, May.
    6. Matsumoto, Hiroyuki & Wesolowski, Jacek & Witkowski, Piotr, 2009. "Tree structured independence for exponential Brownian functionals," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3798-3815, October.
    7. Piliszek, Agnieszka & Wesołowski, Jacek, 2016. "Kummer and gamma laws through independences on trees—Another parallel with the Matsumoto–Yor property," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 15-27.
    8. Wesołowski, Jacek, 2015. "On the Matsumoto–Yor type regression characterization of the gamma and Kummer distributions," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 145-149.
    9. Bartosz Kołodziejek, 2017. "The Matsumoto–Yor Property and Its Converse on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 30(2), pages 624-638, June.

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