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On the limit distributions of continuous-state branching processes with immigration

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  • Keller-Ressel, Martin
  • Mijatović, Aleksandar
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    Abstract

    We consider the class of continuous-state branching processes with immigration (CBI-processes), introduced by Kawazu and Watanabe (1971) [10] and their limit distributions as time tends to infinity. We determine the Lévy–Khintchine triplet of the limit distribution and give an explicit description in terms of the characteristic triplet of the Lévy subordinator and the scale function of the spectrally positive Lévy process, which describe the immigration resp. branching mechanism of the CBI-process. This representation allows us to describe the support of the limit distribution and characterize its absolute continuity and asymptotic behavior at the boundary of the support, generalizing several known results on self-decomposable distributions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 122 (2012)
    Issue (Month): 6 ()
    Pages: 2329-2345

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    Handle: RePEc:eee:spapps:v:122:y:2012:i:6:p:2329-2345

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    Related research

    Keywords: Branching processes with immigration; Limit distribution; Stationary distribution; Self-decomposable distribution; Spectrally positive Lévy process; Scale function; Infinitesimal generator;

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    1. Sato, Ken-iti & Yamazato, Makoto, 1984. "Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type," Stochastic Processes and their Applications, Elsevier, vol. 17(1), pages 73-100, May.
    2. Masuda, H. & Yoshida, N., 2005. "Asymptotic expansion for Barndorff-Nielsen and Shephard's stochastic volatility model," Stochastic Processes and their Applications, Elsevier, vol. 115(7), pages 1167-1186, July.
    3. Martin Keller-Ressel & Thomas Steiner, 2008. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models," Finance and Stochastics, Springer, vol. 12(2), pages 149-172, April.
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