On Seneta's constants for the supercritical Bellman-Harris process with $E(Z_+ \log Z_+) = \infty$

Wolfgang P. Angerer

On Seneta's constants for the supercritical Bellman-Harris process with $E(Z_+ \log Z_+) = \infty$

Probability 2007-05-23 v2

Authors: Wolfgang P. Angerer

Abstract

For a finite mean supercriticial Bellman-Harris process, there exist numbers $\chi_t$ (the Seneta constants) such that $\chi_t$ times the size of the population at time $t$ converges almost surely to a non-degenerate limit. We obtain a characterisation of the slowly varying part of the Seneta constants under the assumption that the life-time distribution of particles is strongly non-lattice.

Keywords

Bellman-Harris process Seneta constants supercritical slowly varying strongly non-lattice

Cite

@article{arxiv.math/0512458,
  title  = {On Seneta's constants for the supercritical Bellman-Harris process with $E(Z_+ \log Z_+) = \infty$},
  author = {Wolfgang P. Angerer},
  journal= {arXiv preprint arXiv:math/0512458},
  year   = {2007}
}

Comments

8 pages, final part of proof rewritten

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