Electronic Journal of Probability

Williams decomposition for superprocesses

Yan-Xia Ren, Renming Song, and Rui Zhang

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Abstract

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.

Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 23, 33 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1519722152

Digital Object Identifier
doi:10.1214/18-EJP146

Subjects
Primary: 60J25: Continuous-time Markov processes on general state spaces 60G55: Point processes 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
superprocesses Williams decomposition spatially dependent branching mechanism genealogy

Rights
Creative Commons Attribution 4.0 International License.

Citation

Ren, Yan-Xia; Song, Renming; Zhang, Rui. Williams decomposition for superprocesses. Electron. J. Probab. 23 (2018), paper no. 23, 33 pp. doi:10.1214/18-EJP146. https://projecteuclid.org/euclid.ejp/1519722152


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