Abstract
In this paper, we consider a class of generalized continuous-state branching processes obtained by Lamperti type time changes of spectrally positive Lévy processes using different rate functions. When explosion occurs to such a process, we show that the process converges to infinity in finite time asymptotically along a deterministic curve, and identify the speed of explosion for rate function in different regimes. To prove the main theorems, we also establish a new asymptotic result for scale function of the spectrally positive Lévy process.
Funding Statement
Bo Li and Xiaowen Zhou are supported by NSERC (RGPIN-2016-06704). Xiaowen Zhou is supported by NSFC (#12171405).
Acknowledgments
The authors thank an anonymous referee for detailed comments and helpful suggestions.
Citation
Bo Li. Xiaowen Zhou. "On the explosion of a class of continuous-state nonlinear branching processes." Electron. J. Probab. 26 1 - 25, 2021. https://doi.org/10.1214/21-EJP715
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