论文标题
在关键情况下，一类连续状态非线性分支过程的边界行为
Boundary behaviors for a class of continuous-state nonlinear branching processes in critical cases
论文作者
论文摘要
使用福斯特裂解技术，我们建立了有关非爆发，非探索的新条件，分别从无穷大降低并保持无限的无限状态，用于在李等人中引入的一般连续状态非线性分支过程。 （2019）。这些结果可以应用于确定上述非线性分支过程的关键案例的边界行为，其功率函数由布朗运动和（或）稳定的泊松随机度量驱动，这在Li等人中保持开放。 （2019）。特别是，我们表明，即使在关键案例中，从无穷大和保持无限之间也会发生相变。
Using Foster-Lyapunov techniques we establish new conditions on non-extinction, non-explosion, coming down from infinity and staying infinite, respectively, for the general continuous-state nonlinear branching processes introduced in Li et al. (2019). These results can be applied to identify boundary behaviors for the critical cases of the above nonlinear branching processes with power rate functions driven by Brownian motion and (or) stable Poisson random measure, which was left open in Li et al. (2019). In particular, we show that even in the critical cases, a phase transition happens between coming down from infinity and staying infinite.
