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- W2772078270 abstract "Consider a supercritical Crump-Mode-Jagers process such that all births are at integer times (the lattice case). We showed in a recent paper that under a certain condition on the generating function of the intensity of the offspring process, the second-order fluctuations of the age distribution are asymptotically normal. In the present paper we study mainly the case when this condition is not satisfied. There are two other cases; in one (boundary) case the fluctuations are still asymptotically normal, but with a larger order of the variance; in the last case, the fluctuations are even larger, but will oscillate and (except in degenerate cases) not converge in distribution. This trichotomy is similar to what has been seen in related situations, e.g. for P$'o$lya urns. We also add some further results in the first case, including a symbolic calculus." @default.
- W2772078270 created "2017-12-22" @default.
- W2772078270 creator A5022615833 @default.
- W2772078270 date "2017-12-06" @default.
- W2772078270 modified "2023-09-27" @default.
- W2772078270 title "Fluctuations in Crump-Mode-Jagers processes: the lattice case" @default.
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