\(R\)-positivity, quasi-stationary distributions and ratio limit theorems for a class of probabilistic automata

DOI10.1214/aoap/1034968146zbMath0855.60061OpenAlexW2001447203MaRDI QIDQ1814753

Pablo A. Ferrari, Harry Kesten, Servet Martínez

Publication date: 31 October 1996

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

Full work available at URL: https://doi.org/10.1214/aoap/1034968146

zbMATH Keywords

central limit theoremabsorbing Markov chainYaglom limitratio limit theoremquasistationary distribution\(R\)-positivity

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

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Cites Work

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• Gaussian fluctuations of connectivities in the subcritical regime of percolation
• Exponential decay for subcritical contact and percolation processes
• Gaussian limit for critical oriented percolation in high dimensions.
• Sharpness of the phase transition in percolation models
• Existence of quasi-stationary distributions: A renewal dynamical approach
• Ergodic properties of nonnegative matrices. I
• Weak convergence of conditioned birth and death processes
• Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state
• A ratio limit theorem for (sub) Markov chains on {1,2, …} with bounded jumps
• On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states

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