126 research outputs found
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 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.Comment: Published at http://dx.doi.org/10.1214/009117906000001015 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
One-dimensional linear recursions with Markov-dependent coefficients
For a class of stationary Markov-dependent sequences
we consider the random linear recursion
and show that the distribution tail of
its stationary solution has a power law decay.Comment: Published at http://dx.doi.org/10.1214/105051606000000844 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
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