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

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

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 (US)
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
State	Published - Feb 1 2020

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

ASJC Scopus subject areas

Applied Mathematics

Online availability

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.",

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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.

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KW - Asymptotic behavior of the survival probability

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KW - Martingale change of measure

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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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