The multi-type Galton-Watson process with immigration
- 1 April 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 7 (02) , 411-422
- https://doi.org/10.1017/s0021900200034975
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
This publication has 4 references indexed in Scilit:
- Functional equations and the Galton-Watson processAdvances in Applied Probability, 1969
- On multitype branching processes with ϱ ⩽ 1Journal of Mathematical Analysis and Applications, 1967
- On the use of the direct matrix product in analysing certain stochastic population modelsBiometrika, 1966
- Nonnegative Square MatricesEconometrica, 1953