Abstract
The critical age-dependent branching process with offspring p.g.f. of the form $f(s) = s + (1 - s)^{1 + \alpha}L(1 - s), 0 < \alpha \leq 1, L$ slowly varying at 0, is investigated. We generalize Kesten's unpublished necessary condition to establish N.A.S.C. on the tail of the lifetime distribution for existence of a nondegenerate normalized conditioned limit law and pose several related questions.
Citation
Martin I. Goldstein. Fred M. Hoppe. "Necessary and Sufficient Lifetime Conditions for Normed Convergence of Critical Age-Dependent Processes with Infinite Variance." Ann. Probab. 9 (3) 490 - 497, June, 1981. https://doi.org/10.1214/aop/1176994421
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