Critical age-dependent branching process diffusions

Warren Esty

Stochastic Processes and their Applications, 1975, vol. 3, issue 2, 209-220

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.

Keywords: age-dependent; branching; process; critical; branching; process; age-dependent; Q-process; diffusions (search for similar items in EconPapers)
Date: 1975
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