8 papers · 1 filter
-stable fluctuation of the derivative martingale of branching random walk
Haojie Hou, Yan-Xia Ren, Renming Song
In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens th…
Limiting distributions for a class of super-Brownian motions with spatially dependent branching mechanisms
Yan-Xia Ren, Ting Yang
In this paper we consider a large class of super-Brownian motions in with spatially dependent branching mechanisms. We establish the almost sure growth rate of the mas…
Lower deviation for the supremum of the support of super-Brownian motion
Yan-Xia Ren, Renming Song, Rui Zhang
We study the asymptotic behavior of the supremum of the support of a supercritical super-Brownian motion. In our recent paper (Stoch. Proc. Appl. 137 (2021), 1-34), we showed…
Weak convergence of the extremes of branching Lévy processes with regularly varying tails
Yan-Xia Ren, Renming Song, Rui Zhang
In this paper, we study the weak convergence of the extremes of supercritical branching Lévy processes whose spatial motions are Lévy processes with regu…
Branching Brownian motion in a periodic environment and existence of pulsating travelling waves
Yan-Xia Ren, Renming Song, Fan Yang
We study the limits of the additive and derivative martingales of one-dimensional branching Brownian motion in a periodic environment. Then we prove the existence of pulsating trav…
Stable Central Limit Theorems for Super Ornstein-Uhlenbeck Processes, II
Yan-Xia Ren, Renming Song, Zhenyao Sun +1
This paper is a continuation of our recent paper (Elect. J. Probab. 24 (2019), no. 141) and is devoted to the asymptotic behavior of a class of supercritical super Ornstein-Uhlenbe…