On Seneta’s Constants for the Supercritical Bellman-Harris Process with E(Z+ log Z+) = ∞
نویسنده
چکیده
For a finite mean supercriticial Bellman-Harris process, let Zt be the number of particles at time t. There exist numbers χt (the Seneta constants) such that χtZt converges almost surely to a non-degenerate limit. Furthermore, χt ∝ e −βt L(e), where β is the Malthusian parameter, and L is slowly varying at zero. We obtain a characterisation of the slowly varying part of the Seneta constants under the assumption that the lifetime distribution of particles is strongly non-lattice.
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تاریخ انتشار 2008