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^*

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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.

源语言	英语
页（从-至）	498-534
页数	37
期刊	Stochastic Processes and their Applications
卷	163
DOI	https://doi.org/10.1016/j.spa.2023.06.008
出版状态	已出版 - 9月 2023

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10.1016/j.spa.2023.06.008

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Liu, R., Ren, Y. X., Song, R., & Sun, Z. (2023). Subcritical superprocesses conditioned on non-extinction. Stochastic Processes and their Applications, 163, 498-534. https://doi.org/10.1016/j.spa.2023.06.008

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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",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2023",

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doi = "10.1016/j.spa.2023.06.008",

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AU - Ren, Yan Xia

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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.

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DO - 10.1016/j.spa.2023.06.008

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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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