The supercritical birth, death and catastrophe process: Limit theorems on the set of non-extinction

DOI10.1007/BF00276370zbMath0721.60093WikidataQ113909097 ScholiaQ113909097MaRDI QIDQ2641012

Anthony G. Pakes

Publication date: 1988

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

zbMATH Keywords

almost sure convergenceslowly varying functionextinction probabilitiessupercritical caselinear birth and death processCatastrophes

Mathematics Subject Classification ID

Strong limit theorems (60F15) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (8)

The Markov branching process with density-independent catastrophes. II. The subcritical and critical cases ⋮ A complementary note on the supercritical birth, death and catastrophe process ⋮ Convergence rates and limit theorems for the dual Markov branching process ⋮ Maximum likelihood estimation in birth-death process allowing catastrophes ⋮ The linear birth and death process under the influence of independently occurring disasters ⋮ Extinction times and size of the surviving species in a two-species competition process ⋮ The Markov branching process with density-independent catastrophes. III. The supercritical case ⋮ The supercritical birth, death and catastrophe process: Limit theorems on the set of extinction

Cites Work

• Unnamed Item
• A modification of the branching process
• The supercritical birth, death and catastrophe process: Limit theorems on the set of extinction
• Limit theorems for the population size of a birth and death process allowing catastrophes
• The extinction time of a birth, death and catastrophe process and of a related diffusion model
• Asymptotic results for the extinction time of Markov branching processes allowing emigration, I. Random walk decrements
• The asymptotic behaviour of birth and death and some related processes

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