A rate of convergence result for the super-critical Galton-Watson process
- 1 April 1970
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 7 (02) , 451-454
- https://doi.org/10.1017/s0021900200035038
Abstract
Let Z0 = 1, Z1, Z2, ··· denote a super-critical Galton-Watson process whose non-degenerate offspring distribution has probability generating function where 1 < m = EZ 1 < ∞. The Galton-Watson process evolves in such a way that the generating function Fn (s) of Zn is the nth functional iterate of F(s). The convergence problem for Z n, when appropriately normed, has been studied by quite a number of authors; for an ultimate form see Heyde [2]. However, no information has previously been obtained on the rate of such convergence. We shall here suppose that in which case Wn = m –nZn converges almost surely to a non-degenerate random variable W as n → ∞ (Harris [1], p. 13). It is our object to establish the following result on the rate of convergence of Wn to W.Keywords
This publication has 0 references indexed in Scilit: