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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
DOI: 10.2307/3211974
Stable URL: http://www.jstor.org/stable/3211974
Page Count: 12
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Multi-Type Galton-Watson Process with Immigration
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Abstract

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.

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