A note on multitype branching processes with immigration in a random environment

Details A note on multitype branching processes with immigration in a random environment A note on multitype branching processes with immigration in a random environment

2005-05-13

arxiv.org/abs/math/0505292v2

Annals of Probability 2007, Vol. 35, No. 4, 1573-1592

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000001015 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

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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