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

Natalia Cardona-Tobón () and Juan Carlos Pardo ()
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Natalia Cardona-Tobón: Georg-August-Universität Göttingen
Juan Carlos Pardo: Centro de Investigación en Matemáticas

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3395-3425

Abstract: 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.

Keywords: Continuous-state branching processes; Lévy processes; Random environment; Long-term behaviour; Explosion; 60J80; 60G51; 60H10; 60K37 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01338-0

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