The Annals of Applied Probability

Multitype branching limit behavior

Harry Cohn and Qiao Wang

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Abstract

For a multitype branching process in varying environment convergent in probability, a certain sequence of linear combinations of the type sizes is shown to possess some convergence properties. This sequence turns out to be instrumental in deriving a condition for continuity of the limiting distribution function. An application to an $L_1$ convergent process whose offspring mean matrices are weakly ergodic is also given.

Article information

Source
Ann. Appl. Probab., Volume 13, Number 2 (2003), 490-500.

Dates
First available in Project Euclid: 18 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1050689590

Digital Object Identifier
doi:10.1214/aoap/1050689590

Mathematical Reviews number (MathSciNet)
MR1970273

Zentralblatt MATH identifier
1030.60079

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

Keywords
Martingale varying environment multitype concentration function continuity space-time harmonic function

Citation

Cohn, Harry; Wang, Qiao. Multitype branching limit behavior. Ann. Appl. Probab. 13 (2003), no. 2, 490--500. doi:10.1214/aoap/1050689590. https://projecteuclid.org/euclid.aoap/1050689590


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References

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  • PARKVILLE, VICTORIA 3052 AUSTRALIA E-MAIL: harry@ms.unimelb.edu.au