Proves convergence of critical multitype Bellman-Harris process with one infinite-mean lifetime to Poisson random measure concentrated on that type under space-lifetime condition ρ > γ/β.
Renewal processes of Mittag-Leffler and Wright type
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abstract
After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding renewal processes with reward and numerically their long-time behaviour.
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2026 1verdicts
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Convergence of a Critical Multitype Bellman--Harris Process with One Infinite-Mean Lifetime
Proves convergence of critical multitype Bellman-Harris process with one infinite-mean lifetime to Poisson random measure concentrated on that type under space-lifetime condition ρ > γ/β.