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The multi-type Galton-Watson process with immigration

Published online by Cambridge University Press:  14 July 2016

M. P. Quine
M. P. Quine*
Affiliation:
Australian National University
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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.

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 411 - 422
Copyright
Copyright © Applied Probability Trust 1970 

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