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Explosion Rates for Continuous-State Branching Processes in a Lévy Environment

Author

Listed:
  • Natalia Cardona-Tobón

    (Georg-August-Universität Göttingen)

  • Juan Carlos Pardo

    (Centro de Investigación en Matemáticas)

Abstract

Here, we study the long-term behaviour of the non-explosion probability for continuous-state branching processes in a Lévy environment when the branching mechanism is given by the negative of the Laplace exponent of a subordinator. In order to do so, we study the law of this family of processes in the infinite mean case and provide necessary and sufficient conditions for the process to be conservative, i.e. that the process does not explode in finite time a.s. In addition, we establish precise rates for the non-explosion probabilities in the subcritical and critical regimes, first found by Palau et al. (ALEA Lat Am J Probab Math Stat 13(2):1235–1258, 2016) in the case when the branching mechanism is given by the negative of the Laplace exponent of a stable subordinator.

Suggested Citation

  • Natalia Cardona-Tobón & Juan Carlos Pardo, 2024. "Explosion Rates for Continuous-State Branching Processes in a Lévy Environment," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3395-3425, November.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:4:d:10.1007_s10959-024-01338-0
    DOI: 10.1007/s10959-024-01338-0
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    References listed on IDEAS

    as
    1. Hui He & Zenghu Li & Wei Xu, 2018. "Continuous-State Branching Processes in Lévy Random Environments," Journal of Theoretical Probability, Springer, vol. 31(4), pages 1952-1974, December.
    2. Li, Zenghu & Xu, Wei, 2018. "Asymptotic results for exponential functionals of Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 108-131.
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