论文标题
频谱负分支莱维过程的最大位移
Maximal displacement of spectrally negative branching Lévy processes
论文作者
论文摘要
我们考虑了在连续时间的分支马尔可夫过程，其中粒子随着频谱负Lévy过程独立发展。当分支机理是关键或亚临界的时，该过程最终将死亡，我们可以定义其总体最大值，即颗粒达到的最大位置。本文的目的是给出该最大生存函数的渐近估计值。特别是，我们表明，在关键情况下，当底层莱维过程振荡或漂移到$+\ infty $时，渐近学是多项式的，当它向$ - \ infty $漂移时，它是指数的。
We consider a branching Markov process in continuous time in which the particles evolve independently as spectrally negative Lévy processes. When the branching mechanism is critical or subcritical, the process will eventually die and we may define its overall maximum, i.e. the maximum location ever reached by a particule. The purpose of this paper is to give asymptotic estimates for the survival function of this maximum. In particular, we show that in the critical case the asymptotics is polynomial when the underlying Lévy process oscillates or drifts towards $+\infty$, and is exponential when it drifts towards $-\infty$.
