The multi-type Galton-Watson process with immigration
- 1 August 1970
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 7 (2), 411-422
- https://doi.org/10.2307/3211974
Abstract
Summary: We consider the limiting behaviour of a k-type (k < ∞) Galton-Watson process which is augmented at each generation by a stochastic immigration component. In Section 2, conditions for ergodicity are found for a subclass of such processes. In Section 3, expressions are derived for the first two moments of the nth generation (by way of a recurrence relation) and for the first two asymptotic moments, in a manner which to some extent generalises previous results.Keywords
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