5 citations · 17 across the 14 of their papers we have counts for
14 papers
Large deviations and almost sure convergence for the extremes of branching Lévy processes
Runjia Luo, Yan-Xia Ren, Renming Song +1
In this paper, we investigate the asymptotic behavior of supercritical branching Markov processes whose spatial motions are Lévy processes with regularly…
Moments of additive martingales of branching Lévy processes and applications
Yan-Xia Ren, Renming Song, Rui Zhang
Let be the Biggins martingale of a supercritical branching Lévy process with non-local branching mechanism, and denote by its limit. In this paper, we first…
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…
The extremal process of super-Brownian motion: a probabilistic approach via skeletons
Yan-Xia Ren, Ting Yang, Rui Zhang
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…
The extremal process of super-Brownian motion
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 th…
Non-integrable stable approximation by Stein's method
Peng Chen, Ivan Nourdin, Lihu Xu +2
We develop Stein's method for -stable approximation with , continuing the recent line of research by Xu \cite{lihu} and Chen, Nourdin and Xu \cite{C-N-X} in the case…
On properties of a class of strong limits for supercritical superprocesses
Yan-Xia Ren, Renming Song, Rui Zhang
Suppose that is a supercritical superprocess in a locally compact separable metric space . Let be a positive eigenfunction corresponding…
Supercritical Superprocesses: Proper Normalization and Non-degenerate Strong Limit
Yan-Xia Ren, Renming Song, Rui Zhang
Suppose that is a supercritical superprocess in a locally compact separable metric space . Let be a positive eigenfunction corresponding…
Williams decomposition for superprocesses
Yan-Xia Ren, Renming Song, Rui Zhang
We decompose the genealogy of a general superprocess with spatially dependent branching mechanism with respect to the last individual alive (Williams decomposition). This is a gene…
Functional central limit theorems for supercritical superprocesses
Yan-Xia Ren, Renming Song, Rui Zhang
In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfyin…
Limit Theorems for Some Critical Superprocesses
Yan-Xia Ren, Renming Song, Rui Zhang
In this paper we establish some conditional limit theorems for some critical superprocesses . First we identify the rate of non-extinction. Then we show that, fo…
Central Limit Theorems for Supercritical Branching Markov Processes
Y. -X. Ren, R. Song, R. Zhang
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These a…
Central Limit Theorems for Super-OU Processes
Yan-Xia Ren, Renming Song, Rui Zhang
In this paper we study supercritical super-OU processes with general branching mechanisms satisfying a second moment condition. We establish central limit theorems for the super-OU…