TY - JOUR
T1 - Subcritical superprocesses conditioned on non-extinction
AU - Liu, Rongli
AU - Ren, Yan Xia
AU - Song, Renming
AU - Sun, Zhenyao
N1 - The research of this project is supported by the National Key R&D Program of China (No. 2020YFA0712900 ).
The research of this project is supported by the National Key R&D Program of China (No. 2020YFA0712900).The research of Rongli Liu is supported in part by NSFC (Grant No. 12271374), and the Fundamental Research Funds for the Central Universities, China (Grant No. 2017RC007).The research of Yan-Xia Ren is supported in part by NSFC (Grant Nos. 12071011, 11731009 and 12231002), and the Fundamental Research Funds for the Central Universities, Peking University LMEQF.The research of Renming Song is supported in part by a grant from the Simons Foundation, United States (#960480, Renming Song).We thank the referees for the helpful comments and suggestions. Part of the research for this paper was done while the third-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China (11931004, Yingchao Xie) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions, China. Part of the research for this paper was down while the fourth-named author was a Postdoc at the Technion—Israel Institute of Technology where he was supported by a fellowship of the Israel Council for Higher Education.
We thank the referees for the helpful comments and suggestions. Part of the research for this paper was done while the third-named author was visiting Jiangsu Normal University, where he was partially supported by a grant from the National Natural Science Foundation of China ( 11931004 , Yingchao Xie) and by the Priority Academic Program Development of Jiangsu Higher Education Institutions, China . Part of the research for this paper was down while the fourth-named author was a Postdoc at the Technion—Israel Institute of Technology where he was supported by a fellowship of the Israel Council for Higher Education .
PY - 2023/9
Y1 - 2023/9
N2 - We consider a class of subcritical superprocesses (Xt)t≥0 with general spatial motions and general branching mechanisms. We study the asymptotic behaviors of Qt,r, the distribution of Xt conditioned on Xt+r not being a null measure. We first give the existence of limt→∞Qt,r and limr→∞Qt,r, and then show that an LlogL-type condition is equivalent to the existence of the iterated limits: limr→∞limt→∞Qt,r and limt→∞limr→∞Qt,r. Finally, when the LlogL-type condition holds, we show that those iterated limits, and the double limit limr,t→∞Qt,r, are the same.
AB - We consider a class of subcritical superprocesses (Xt)t≥0 with general spatial motions and general branching mechanisms. We study the asymptotic behaviors of Qt,r, the distribution of Xt conditioned on Xt+r not being a null measure. We first give the existence of limt→∞Qt,r and limr→∞Qt,r, and then show that an LlogL-type condition is equivalent to the existence of the iterated limits: limr→∞limt→∞Qt,r and limt→∞limr→∞Qt,r. Finally, when the LlogL-type condition holds, we show that those iterated limits, and the double limit limr,t→∞Qt,r, are the same.
UR - https://www.scopus.com/pages/publications/85164228351
UR - https://www.scopus.com/pages/publications/85164228351#tab=citedBy
U2 - 10.1016/j.spa.2023.06.008
DO - 10.1016/j.spa.2023.06.008
M3 - Article
AN - SCOPUS:85164228351
SN - 0304-4149
VL - 163
SP - 498
EP - 534
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
ER -