Stochastic Processes and their Applications ( IF 1.4 ) Pub Date : 2021-03-26 , DOI: 10.1016/j.spa.2021.03.007 Yan-Xia Ren , Renming Song , Rui Zhang
In this paper, we establish limit theorems for the supremum of the support, denoted by , of a supercritical super-Brownian motion on . We prove that there exists an such that converges in law, and give some large deviation results for as . We also prove that the limit of the extremal process is a Poisson random measure with exponential intensity in which each atom is decorated by an independent copy of an auxiliary measure. These results are analogues of the results for branching Brownian motions obtained in Arguin et al. (2013), Aïdékon et al. (2013) and Roberts (2013).
中文翻译:
超布朗运动的极值过程
在本文中,我们建立了支撑的最大极限定理,表示为 ,超临界超布朗运动 上 。我们证明存在一个 这样 在法律上收敛,并给出一些大的偏差结果 作为 。我们还证明了极限过程的极限是具有指数强度的泊松随机测度,其中每个原子都由独立的辅助测度副本修饰。这些结果与Arguin等人获得的分支布朗运动的结果类似。(2013),Aïdékon等人。(2013)和罗伯茨(2013)。