Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses

Yan Xia Ren; Renming Song; Zhenyao Sun

doi:10.1007/s10440-019-00243-7

Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses

Yan Xia Ren
, Renming Song
, Zhenyao Sun^*

^*此作品的通讯作者

Peking University
University of Illinois at Urbana-Champaign

科研成果: 期刊稿件 › 文章 › 同行评审

9 引用（Scopus）

摘要

In this paper we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yaglom’s exponential limit law for critical superprocesses.

源语言	英语
页（从-至）	91-131
页数	41
期刊	Acta Applicandae Mathematicae
卷	165
期	1
DOI	https://doi.org/10.1007/s10440-019-00243-7
出版状态	已出版 - 1 2月 2020
已对外发布	是

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abstract = "In this paper we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yaglom{\textquoteright}s exponential limit law for critical superprocesses.",

keywords = "2-Spine decomposition, Asymptotic behavior of the survival probability, Critical superprocess, Martingale change of measure, Size-biased Poisson random measure, Spine decomposition, Yaglom{\textquoteright}s exponential limit law",

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note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature B.V.",

year = "2020",

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doi = "10.1007/s10440-019-00243-7",

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T1 - Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses

AU - Ren, Yan Xia

AU - Song, Renming

AU - Sun, Zhenyao

PY - 2020/2/1

Y1 - 2020/2/1

N2 - In this paper we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yaglom’s exponential limit law for critical superprocesses.

AB - In this paper we first establish a decomposition theorem for size-biased Poisson random measures. As consequences of this decomposition theorem, we get a spine decomposition theorem and a 2-spine decomposition theorem for some critical superprocesses. Then we use these spine decomposition theorems to give probabilistic proofs of the asymptotic behavior of the survival probability and Yaglom’s exponential limit law for critical superprocesses.

KW - 2-Spine decomposition

KW - Asymptotic behavior of the survival probability

KW - Critical superprocess

KW - Martingale change of measure

KW - Size-biased Poisson random measure

KW - Spine decomposition

KW - Yaglom’s exponential limit law

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DO - 10.1007/s10440-019-00243-7

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VL - 165

SP - 91

EP - 131

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 1

ER -

Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses

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