论文标题
超棕色运动的极端过程：通过骨骼的概率方法
The extremal process of super-Brownian motion: a probabilistic approach via skeletons
论文作者
论文摘要
最近，Ren等。 [Stoch。 Proc。 Appl。，137（2021）]已证明，超棕色运动的极端过程在大时的限制下分布在分布中收敛。他们的技术在很大程度上依赖于沿[M.布兰森，mem。阿米尔。数学。 Soc。，44（1983）]。在本文中，我们采用了另一种方法。我们的方法是基于超棕色运动的骨架分解。骨骼可以解释为确定该过程较大时间行为的不朽颗粒。我们利用这一事实，并将渐近特性从骨骼到超棕色运动。获得了有关限制过程的概率表示的一些新结果，这些结果无法直接通过[Y.-x的结果直接获得。 Ren等，Stoch。 Proc。 Appl。，137（2021）]。除结果外，我们的方法还深入了解了超青褐色动议的限制过程的推动力。
Recently Ren et al. [Stoch. Proc. Appl., 137 (2021)] have proved that the extremal process of the super-Brownian motion converges in distribution in the limit of large times. Their techniques rely heavily on the study of the convergence of solutions to the Kolmogorov-Petrovsky-Piscounov equation along the lines of [M. Bramson, Mem. Amer. Math. Soc., 44 (1983)]. In this paper we take a different approach. Our approach is based on the skeleton decomposition of super-Brownian motion. The skeleton may be interpreted as immortal particles that determine the large time behaviour of the process. We exploit this fact and carry asymptotic properties from the skeleton over to the super-Brownian motion. Some new results concerning the probabilistic representations of the limiting process are obtained, which cannot be directly obtained through the results of [Y.-X. Ren et al., Stoch. Proc. Appl., 137 (2021)]. Apart from the results, our approach offers insights into the driving force behind the limiting process for super-Brownian motions.
