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2018 Williams decomposition for superprocesses
Yan-Xia Ren, Renming Song, Rui Zhang
Electron. J. Probab. 23: 1-33 (2018). DOI: 10.1214/18-EJP146


We decompose the genealogy of a general superprocess with spatially dependent branching mechanism with respect to the last individual alive (Williams decomposition). This is a generalization of the main result of Delmas and Hénard [5] where only superprocesses with spatially dependent quadratic branching mechanism were considered. As an application of the Williams decomposition, we prove that, for some superprocesses, the normalized total measure will converge to a point measure at its extinction time. This partially generalizes a result of Tribe [27] in the sense that our branching mechanism is more general.


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Yan-Xia Ren. Renming Song. Rui Zhang. "Williams decomposition for superprocesses." Electron. J. Probab. 23 1 - 33, 2018.


Received: 12 September 2016; Accepted: 29 January 2018; Published: 2018
First available in Project Euclid: 27 February 2018

zbMATH: 1387.60118
MathSciNet: MR3771760
Digital Object Identifier: 10.1214/18-EJP146

Primary: 60G55 , 60J25 , 60J80

Keywords: genealogy , spatially dependent branching mechanism , Superprocesses , Williams decomposition


Vol.23 • 2018
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