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Continuous branching processes and spectral positivity

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  • Bingham, N. H.

Abstract

Certain properties of continuous-state branching processes are studied via the random time-change linking them with spectrally positive Lévy processes. The results are compared and contrasted with those for simple branching processes.

Suggested Citation

  • Bingham, N. H., 1976. "Continuous branching processes and spectral positivity," Stochastic Processes and their Applications, Elsevier, vol. 4(3), pages 217-242, August.
    • Handle: RePEc:eee:spapps:v:4:y:1976:i:3:p:217-242
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    Cited by:

    1. Mijatović, Aleksandar & Vidmar, Matija & Jacka, Saul, 2015. "Markov chain approximations to scale functions of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3932-3957.
    2. 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.
    3. Anthony G. Pakes, 2020. "Self-Decomposable Laws from Continuous Branching Processes," Journal of Theoretical Probability, Springer, vol. 33(1), pages 361-395, March.
    4. Palau, S. & Pardo, J.C., 2017. "Continuous state branching processes in random environment: The Brownian case," Stochastic Processes and their Applications, Elsevier, vol. 127(3), pages 957-994.
    5. Abraham, Romain & Delmas, Jean-François & He, Hui, 2021. "Some properties of stationary continuous state branching processes," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 309-343.
    6. Zenghu Li & Chunhua Ma, 2008. "Catalytic Discrete State Branching Models and Related Limit Theorems," Journal of Theoretical Probability, Springer, vol. 21(4), pages 936-965, December.
    7. Duquesne, Thomas, 2009. "Continuum random trees and branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 119(1), pages 99-129, January.
    8. Florin Avram & Andras Horváth & Serge Provost & Ulyses Solon, 2019. "On the Padé and Laguerre–Tricomi–Weeks Moments Based Approximations of the Scale Function W and of the Optimal Dividends Barrier for Spectrally Negative Lévy Risk Processes," Risks, MDPI, vol. 7(4), pages 1-24, December.
    9. Foucart, Clément & Möhle, Martin, 2022. "Asymptotic behaviour of ancestral lineages in subcritical continuous-state branching populations," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 510-531.
    10. Duquesne, Thomas, 2012. "The exact packing measure of Lévy trees," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 968-1002.
    11. Duquesne, Thomas & Winkel, Matthias, 2019. "Hereditary tree growth and Lévy forests," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3690-3747.

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