The multi-type Galton-Watson process with immigration

1970/08/01 by M. P. Quine · 3 citations
Mathematics · Economics, Econometrics and Finance · Computer Science · #Stochastic processes and statistical mechanics #Stochastic processes and financial applications #Bayesian Methods and Mixture Models

paper · doi: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 n th 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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