Extinction times for a general birth, death and catastrophe process

DOI10.1239/jap/1101840567zbMath1063.60106OpenAlexW2096697803MaRDI QIDQ4660546

Benjamin J. Cairns, Philip K. Pollett

Publication date: 4 April 2005

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/8b0ce885d7b2e7b70eb3f74350c609069aa6253a

zbMATH Keywords

persistence timehitting timecatastrophe process

Mathematics Subject Classification ID

Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Continuous-time Markov processes on discrete state spaces (60J27) General biology and biomathematics (92B05)

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Extinction time in growth models subject to geometric catastrophes ⋮ A continuous-time Ehrenfest model with catastrophes and its jump-diffusion approximation ⋮ Stationary distributions of semistochastic processes with disturbances at random times and with random severity ⋮ Constructing transient birth-death processes by means of suitable transformations ⋮ The Batch Markovian Arrival Process Subject to Renewal Generated Geometric Catastrophes ⋮ A Class of Multidimensional Q-Processes ⋮ A Note on Extinction Times for the General Birth, Death and Catastrophe Process ⋮ A generating function approach to Markov chains undergoing binomial catastrophes ⋮ On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes

Cites Work

• Unnamed Item
• Dynamics of metapopulations with demographic stochasticity and environmental catastrophes
• Denumerable Markov processes and the associated contraction semigroups on l
• A modification of the branching process
• Limit theorems for the population size of a birth and death process allowing catastrophes
• Continuous-time Markov chains. An applications-oriented approach
• 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
• Birth, immigration and catastrophe processes
• The expected time until absorption when absorption is not certain
• Asymptotic properties of the stationary measure of a Markov branching process
• Uniqueness criteria for continuous-time Markov chains with general transition structures