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

Wolfgang P. Angerer

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

Wolfgang P. Angerer

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Abstract

For a finite mean supercriticial Bellman-Harris process, there exist numbers $χ_t$ (the Seneta constants) such that $χ_t$ 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.

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BibTeX RIS

Wolfgang P. Angerer. 2006-01-10. On Seneta's constants for the supercritical Bellman-Harris process with $E(Z_+ \log Z_+) = \infty$. https://arxiv.org/abs/math/0512458

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