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

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.