Electronic Communications in Probability

General branching processes conditioned on extinction are still branching processes

Peter Jagers and Andreas Lagerås

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Abstract

It is well known that a simple, supercritical Bienaymé-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where child-bearing may occur at different ages, life span may depend upon reproduction, and the whole course of events is thus affected by conditioning upon extinction.

Article information

Source
Electron. Commun. Probab., Volume 13 (2008), paper no. 51, 540-547.

Dates
Accepted: 19 October 2008
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465233478

Digital Object Identifier
doi:10.1214/ECP.v13-1419

Mathematical Reviews number (MathSciNet)
MR2453547

Zentralblatt MATH identifier
1189.60158

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
supercritical subcritical extinction multi-type branching process general branching process Crump-Mode-Jagers process

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Jagers, Peter; Lagerås, Andreas. General branching processes conditioned on extinction are still branching processes. Electron. Commun. Probab. 13 (2008), paper no. 51, 540--547. doi:10.1214/ECP.v13-1419. https://projecteuclid.org/euclid.ecp/1465233478


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References

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