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Some new limit theorems for the critical branching process allowing immigration

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  • Pakes, A. G.

Abstract

Some limit theorems are obtained for the population size of a critical Bienaymé-Galton-Watson process allowing immigration and where the variance of the offspring distribution is infinite. An application is given to a limit theorem for the situation where the immigration does not occur but the population size is conditioned on non-extinction until the remote future. This complements a well-known result of Slack.

Suggested Citation

  • Pakes, A. G., 1976. "Some new limit theorems for the critical branching process allowing immigration," Stochastic Processes and their Applications, Elsevier, vol. 4(2), pages 175-185, April.
    • Handle: RePEc:eee:spapps:v:4:y:1976:i:2:p:175-185
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