On time scales and quasi-stationary distributions for multitype birth-and-death processes

DOI10.1214/18-AIHP948zbMath1434.60237arXiv1702.05369MaRDI QIDQ2291970

Pierre Collet, Jean Rene Chazottes, Sylvie Méléard

Publication date: 31 January 2020

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.05369

zbMATH Keywords

differential equationsLyapunov functionscompetition modelsMarkov jump processpopulation ecologymean time to extinction

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Ecology (92D40) Jump processes on discrete state spaces (60J74)

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Cites Work

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• Unnamed Item
• Random models in ecology and evolution
• Metastable states, quasi-stationary distributions and soft measures
• Estimates on the amplitude of the first Dirichlet eigenvector in discrete frameworks
• A microscopic interpretation for adaptive dynamics trait substitution sequence models
• Exponential convergence to quasi-stationary distribution and \(Q\)-process
• Sharp asymptotics for the quasi-stationary distribution of birth-and-death processes
• Quasi-Stationary Distributions
• WKB theory of large deviations in stochastic populations
• Solutions of ordinary differential equations as limits of pure jump markov processes
• On quantitative convergence to quasi-stationarity

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