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^*

^*Corresponding author for this work

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

9 Citations (Scopus)

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’s exponential limit law for critical superprocesses.

Original language	English
Pages (from-to)	91-131
Number of pages	41
Journal	Acta Applicandae Mathematicae
Volume	165
Issue number	1
DOIs	https://doi.org/10.1007/s10440-019-00243-7
Publication status	Published - 1 Feb 2020
Externally published	Yes

Keywords

2-Spine decomposition
Asymptotic behavior of the survival probability
Critical superprocess
Martingale change of measure
Size-biased Poisson random measure
Spine decomposition
Yaglom’s exponential limit law

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10.1007/s10440-019-00243-7

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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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AU - Song, Renming

AU - Sun, Zhenyao

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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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Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses

Abstract

Keywords

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