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

Peking University
University of Illinois at Urbana-Champaign

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

Access to Document

10.1007/s10440-019-00243-7

Cite this

@article{c54efec63d164fecbca6b71adeb2e633,

title = "Spine Decompositions and Limit Theorems for a Class of Critical Superprocesses",

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",

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

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

year = "2020",

month = feb,

day = "1",

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

language = "English",

volume = "165",

pages = "91--131",

journal = "Acta Applicandae Mathematicae",

issn = "0167-8019",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

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

UR - https://www.scopus.com/pages/publications/85061250771

U2 - 10.1007/s10440-019-00243-7

DO - 10.1007/s10440-019-00243-7

M3 - Article

AN - SCOPUS:85061250771

SN - 0167-8019

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this