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The existence of moments of the conditioned limit of the subcritical Crump-Mode-Jagers branching process

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  • Bagley, J. H.

Abstract

If Z (t) is the sum of the characteristics at time t of the population in a Crump-Mode-Jagers branching process, and T is the time to extinction, it is known that under certain conditions, the distribution of Z (t) conditioned on {T > t} converges to a proper distribution as t-->[infinity]. We derive necessary and sufficient conditions in terms of the offspring process, for the existence of integral moments of this limit distribution.

Suggested Citation

  • Bagley, J. H., 1985. "The existence of moments of the conditioned limit of the subcritical Crump-Mode-Jagers branching process," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 333-341, September.
    • Handle: RePEc:eee:spapps:v:20:y:1985:i:2:p:333-341
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