The Annals of Probability
- Ann. Probab.
- Volume 35, Number 4 (2007), 1573-1592.
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.
Ann. Probab., Volume 35, Number 4 (2007), 1573-1592.
First available in Project Euclid: 8 June 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K37: Processes in random environments
Secondary: 60F05: Central limit and other weak theorems 60F15: Strong theorems
Roitershtein, Alexander. A note on multitype branching processes with immigration in a random environment. Ann. Probab. 35 (2007), no. 4, 1573--1592. doi:10.1214/009117906000001015. https://projecteuclid.org/euclid.aop/1181334253