On the explosion of a class of continuous-state nonlinear branching processes

Bo Li; Xiaowen Zhou

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arXiv · 1910.05914

On the explosion of a class of continuous-state nonlinear branching processes

Bo Li·Xiaowen Zhou

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Abstract

In this paper, we consider a class of generalized continuous-state branching processes obtained by Lamperti type time changes of spectrally positive L\'evy 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 spectrally positive L\'evy process.

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Bo Li, Xiaowen Zhou. 2019-10-14. On the explosion of a class of continuous-state nonlinear branching processes. https://arxiv.org/abs/1910.05914

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