Spine decomposition and L log L criterion for superprocesses with non-local branching mechanisms

Yan Xia Ren; Renming Song; Ting Yang

doi:10.30757/ALEA.V19-08

Spine decomposition and L log L criterion for superprocesses with non-local branching mechanisms

Yan Xia Ren^*, Renming Song^*, Ting Yang^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

In this paper, we provide a pathwise spine decomposition for superprocesses with both local and non-local branching mechanisms under a martingale change of measure. This result complements earlier results established for superprocesses with purely local branching mechanisms and for multitype superprocesses. As an application of this decomposition, we obtain necessary/sufficient conditions for the limit of the fundamental martingale to be non-degenerate. In particular, we obtain extinction properties of superprocesses with non-local branching mechanisms as well as a Kesten-Stigum Llog L theorem for the fundamental martingale.

Original language	English
Pages (from-to)	163-208
Number of pages	46
Journal	Alea
Volume	19
Issue number	1
DOIs	https://doi.org/10.30757/ALEA.V19-08
Publication status	Published - 2022
Externally published	Yes

Keywords

Local branching mechanism
Martingale
Non-local branching mechanism
Spine decomposition
Superprocess
Weak local extinction

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10.30757/ALEA.V19-08

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Ren, Y. X., Song, R., & Yang, T. (2022). Spine decomposition and L log L criterion for superprocesses with non-local branching mechanisms. Alea, 19(1), 163-208. https://doi.org/10.30757/ALEA.V19-08

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AU - Ren, Yan Xia

AU - Song, Renming

AU - Yang, Ting

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AB - In this paper, we provide a pathwise spine decomposition for superprocesses with both local and non-local branching mechanisms under a martingale change of measure. This result complements earlier results established for superprocesses with purely local branching mechanisms and for multitype superprocesses. As an application of this decomposition, we obtain necessary/sufficient conditions for the limit of the fundamental martingale to be non-degenerate. In particular, we obtain extinction properties of superprocesses with non-local branching mechanisms as well as a Kesten-Stigum Llog L theorem for the fundamental martingale.

KW - Local branching mechanism

KW - Martingale

KW - Non-local branching mechanism

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KW - Superprocess

KW - Weak local extinction

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SP - 163

EP - 208

JO - Alea

JF - Alea

IS - 1

ER -

Spine decomposition and L log L criterion for superprocesses with non-local branching mechanisms

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Keywords

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