TY - JOUR
T1 - Subcritical superprocesses conditioned on non-extinction
AU - Liu, Rongli
AU - Ren, Yan Xia
AU - Song, Renming
AU - Sun, Zhenyao
N1 - Publisher Copyright:
© 2023 Elsevier B.V.
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
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 -