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Critical age-dependent branching process diffusions

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  • Esty, Warren

Abstract

Two diffusions are derived as the limits in finite dimensional distributions of appropriately conditioned and scaled critical age-dependent branching processes. A technical lemma about the asymptotic behavior of the joint generating function is used to overcome the difficulties introduced by the non-Markov nature of the process. The results are extensions of those of Lamperti and Ney [5] for Galton-Watson processes. Also, the "age-dependent Q-process" is defined and its transition probabilities obtained.

Suggested Citation

  • Esty, Warren, 1975. "Critical age-dependent branching process diffusions," Stochastic Processes and their Applications, Elsevier, vol. 3(2), pages 209-220, April.
    • Handle: RePEc:eee:spapps:v:3:y:1975:i:2:p:209-220
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