Subcritical superprocesses conditioned on non-extinction

Rongli Liu; Yan Xia Ren; Renming Song; Zhenyao Sun

doi:10.1016/j.spa.2023.06.008

Subcritical superprocesses conditioned on non-extinction

Rongli Liu
, Yan Xia Ren
, Renming Song
, Zhenyao Sun^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Jiaotong University
Peking University
University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a class of subcritical superprocesses (X_t)_t≥0 with general spatial motions and general branching mechanisms. We study the asymptotic behaviors of Q_t,r, the distribution of X_t conditioned on X_t+r not being a null measure. We first give the existence of lim_t→∞Q_t,r and lim_r→∞Q_t,r, and then show that an LlogL-type condition is equivalent to the existence of the iterated limits: lim_r→∞lim_t→∞Q_t,r and lim_t→∞lim_r→∞Q_t,r. Finally, when the LlogL-type condition holds, we show that those iterated limits, and the double limit lim_r,t→∞Q_t,r, are the same.

Original language	English
Pages (from-to)	498-534
Number of pages	37
Journal	Stochastic Processes and their Applications
Volume	163
DOIs	https://doi.org/10.1016/j.spa.2023.06.008
Publication status	Published - Sept 2023

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title = "Subcritical superprocesses conditioned on non-extinction",

abstract = "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.",

author = "Rongli Liu and Ren, \{Yan Xia\} and Renming Song and Zhenyao Sun",

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T1 - Subcritical superprocesses conditioned on non-extinction

AU - Liu, Rongli

AU - Ren, Yan Xia

AU - Song, Renming

AU - Sun, Zhenyao

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 -

Subcritical superprocesses conditioned on non-extinction

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