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The Multi-Type Galton-Watson Process with Immigration
M. P. Quine
Journal of Applied Probability
Vol. 7, No. 2 (Aug., 1970), pp. 411-422
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3211974
Page Count: 12
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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.
Journal of Applied Probability © 1970 Applied Probability Trust