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

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

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 …