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On the hitting times of continuous-state branching processes with immigration

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  • Duhalde, Xan
  • Foucart, Clément
  • Ma, Chunhua

Abstract

We study a two-dimensional joint distribution related to the first passage time below a level for a continuous-state branching process with immigration. We provide an explicit expression of its Laplace transform and obtain a necessary and sufficient criterion for transience or recurrence. We follow the approach of Shiga (1990), by finding some λ-invariant functions for the generator.

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  • Duhalde, Xan & Foucart, Clément & Ma, Chunhua, 2014. "On the hitting times of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4182-4201.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:12:p:4182-4201
    DOI: 10.1016/j.spa.2014.07.019
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    References listed on IDEAS

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    1. Bingham, N. H., 1976. "Continuous branching processes and spectral positivity," Stochastic Processes and their Applications, Elsevier, vol. 4(3), pages 217-242, August.
    2. Keller-Ressel, Martin & Mijatović, Aleksandar, 2012. "On the limit distributions of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 122(6), pages 2329-2345.
    3. 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.
    4. Patie, Pierre, 2005. "On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 593-607, April.
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    Cited by:

    1. Le, V., 2022. "On the extinction of continuous state branching processes with competition," Statistics & Probability Letters, Elsevier, vol. 185(C).
    2. Möhle, Martin & Vetter, Benedict, 2023. "Scaling limits for a class of regular Ξ-coalescents," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 387-422.
    3. Li, Pei-Sen, 2019. "A continuous-state polynomial branching process," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2941-2967.
    4. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Working Papers hal-01275397, HAL.
    5. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR model with branching processes in sovereign interest rate modeling," Finance and Stochastics, Springer, vol. 21(3), pages 789-813, July.
    6. Vidmar, Matija, 2023. "Complete monotonicity of time-changed Lévy processes at first passage," Statistics & Probability Letters, Elsevier, vol. 193(C).
    7. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Post-Print hal-01275397, HAL.
    8. Murillo-Salas, A. & Pérez, J.L. & Siri-Jégousse, A., 2017. "Refracted continuous-state branching processes: Self-regulating populations," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 34-44.
    9. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Papers 1602.05541, arXiv.org, revised Feb 2016.
    10. Foucart, Clément & Vidmar, Matija, 2024. "Continuous-state branching processes with collisions: First passage times and duality," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    11. F. Avram & P. Patie & J. Wang, 2019. "Purely Excessive Functions and Hitting Times of Continuous-Time Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 391-399, June.
    12. Friesen, Martin & Jin, Peng & Rüdiger, Barbara, 2020. "Existence of densities for multi-type continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5426-5452.

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