AI 中文总结
该研究建立了超临界分支布朗运动和超布朗运动中两类鞅小值概率的渐近结果，推广了相关分支过程的已有结论，且与已有文献结果吻合。
AI 中文摘要
本文建立了超临界分支布朗运动和超布朗运动中加法鞅与导数鞅的小值概率的渐近行为，从而推广了Galton--Watson过程和连续状态分支过程的相应结果。对于分支布朗运动中的导数鞅，我们的结果也与Arguin等人的arXiv版本[arXiv:1008.4386 v1]以及Hu[Ann. Inst. H. Poincaré Probab. Stat., 2016]的研究结果一致。
英文摘要
In this paper, we establish asymptotics for the small value probabilities of additive and derivative martingales in both supercritical branching Brownian motions and super Brownian motions, thereby extending the corresponding results for Galton--Watson processes and continuous-state branching processes. For the derivative martingale in branching Brownian motion, our result also agrees with the findings in the arXiv version of Arguin et al. [arXiv:1008.4386 v1] and with those of Hu [Ann. Inst. H. Poincaré Probab. Stat., 2016].
Comments12 pages
