Abstract
Consider a Galton-Watson process in which each individual reproduces independently of all others and has probability aj (j = 0, l, …) of giving rise to j progeny in the following generation and in which there is an independent immigration component where bj (j = 0, l, …) is the probability that j individuals enter the population at each generation. Then letting Xn (n = 0, l, …) be the population size of the n-th generation, it is known (Heathcote [4], [51]) that {Xn} defines a Markov chain on the non-negative integers. Unless otherwise stated, we shall consider only those offspring and immigration distributions that make the Markov chain {Xn} irreducible and aperiodic.
Publisher
Cambridge University Press (CUP)
Reference7 articles.
1. A branching process allowing immigration;Heathcote;J. Roy. Stat. Soc.,1966
2. The Theory of Branching Processes
3. The stationary distribution of a branching process allowing immigration: a remark on the critical case;Seneta;J. Roy. Stat. Soc.,1968
4. The Galton-Watson process with mean one and finite variance;Kesten;Teor. Veroyatnost. i Primenen.,1966
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