Backbone decomposition for continuous-state branching processes with immigration

Andreas E Kyprianou; Y X Ren

doi:10.1016/j.spl.2011.09.013

Backbone decomposition for continuous-state branching processes with immigration

Andreas E Kyprianou, Y X Ren

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Abstract

In the spirit of Duquesne and Winkel (2007) and Berestycki et al. (2011), we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equivalent in law to a continuous-time Galton-Watson process with immigration (with Poissonian dressing). The result also helps to characterise the limiting backbone decomposition which is predictable from the work on consistent growth of Galton-Watson trees with immigration in Cao and Winkel (2010).

Original language	English
Pages (from-to)	139-144
Number of pages	6
Journal	Statistics & Probability Letters
Volume	82
Issue number	1
DOIs	https://doi.org/10.1016/j.spl.2011.09.013
Publication status	Published - Jan 2012

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10.1016/j.spl.2011.09.013

Kyprianou_SPL_2012_82_1_139.pdf
NOTICE: this is the author’s version of a work that was accepted for publication in Statistics & Probability Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Statistics & Probability Letters, vol 82, issue 1, 2012, DOI 10.1016/j.spl.2011.09.013
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Cite this

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AB - In the spirit of Duquesne and Winkel (2007) and Berestycki et al. (2011), we show that supercritical continuous-state branching process with a general branching mechanism and general immigration mechanism is equivalent in law to a continuous-time Galton-Watson process with immigration (with Poissonian dressing). The result also helps to characterise the limiting backbone decomposition which is predictable from the work on consistent growth of Galton-Watson trees with immigration in Cao and Winkel (2010).

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Backbone decomposition for continuous-state branching processes with immigration

Abstract

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