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July 2007 A note on multitype branching processes with immigration in a random environment
Alexander Roitershtein
Ann. Probab. 35(4): 1573-1592 (July 2007). DOI: 10.1214/009117906000001015


We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344–353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344–353], the branching process is subcritical in the sense that it converges to a proper limit law. We complement this result by a strong law of large numbers and a central limit theorem for the partial sums of the process. In addition, we study the asymptotic behavior of oscillations of the branching process, that is, of the random segments between successive times when the extinction occurs and the process starts again with the next wave of the immigration.


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Alexander Roitershtein. "A note on multitype branching processes with immigration in a random environment." Ann. Probab. 35 (4) 1573 - 1592, July 2007.


Published: July 2007
First available in Project Euclid: 8 June 2007

zbMATH: 1117.60079
MathSciNet: MR2330980
Digital Object Identifier: 10.1214/009117906000001015

Primary: 60J80, 60K37
Secondary: 60F05, 60F15

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.35 • No. 4 • July 2007
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