A note on the probability of extinction in a class of population-size-dependent Galton-Watson processes
- 1 June 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 22 (04) , 920-925
- https://doi.org/10.1017/s0021900200108150
Abstract
In a class of population-size-dependent Galton-Watson processes where extinction does not occur with probability 1 we describe the rate of decay of qi (the probability that the process starting from i ancestors will become extinct) as the number i of ancestors increases. The results are related to the asymptotic behavior of the Green's function of the critical Galton-Watson process with immigration.Keywords
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