A note on multitype branching processes with immigration in a random environment
نویسنده
چکیده
We consider a multitype branching process with immigration in a random environment introduced by Key in [12]. It was shown by Key that 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, i.e. of the random segments between successive times when the extinction occurs and the process starts afresh with the next wave of the immigration. MSC2000: primary 60J80, 60K37; secondary 60F05, 60F15.
منابع مشابه
A NOTE ON MULTITYPE BRANCHING PROCESSES WITH IMMIGRATION IN A RANDOM ENVIRONMENT BY ALEXANDER ROITERSHTEIN University of British Columbia
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...
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