Limit theorems for critical branching processes in a finite-state-space Markovian environment

DOI10.1017/apr.2021.18zbMath1486.60110OpenAlexW4206894754WikidataQ113858386 ScholiaQ113858386MaRDI QIDQ5066875

Ronan Lauvergnat, I. G. Grama, Emile Le Page

Publication date: 31 March 2022

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

Full work available at URL: https://doi.org/10.1017/apr.2021.18

zbMATH Keywords

critical branching processMarkovian environmentconditioned limit theoremsYaglom-type theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Cites Work

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• On the survival probability of a branching process in a finite state i.i.d. environment
• On the Markov renewal theorem
• A conditional function limit theorem for a critical branching process in a random medium
• Limit theorems for subcritical branching processes in random environment.
• Limit theorems for affine Markov walks conditioned to stay positive
• Limit theorems for Markov walks conditioned to stay positive under a spectral gap assumption
• On the survival probability of a branching process in a random environment
• The survival probability of critical and subcritical branching processes in finite state space Markovian environment
• Conditioned local limit theorems for random walks defined on finite Markov chains
• Conditioned limit theorems for products of random matrices
• Propriétés asymptotiques des processus de branchement en environnement aléatoire
• On the Theory of Markov Renewal
• Bounds on the extinction time distribution of a branching process
• On the Asymptotic Behavior of the Probability of Non-Extinction for Critical Branching Processes in a Random Environment
• The Survival Probability of a Critical Branching Process in a Random Environment
• On the Survival Probability of a Branching Process in a Random Environment
• Limit theorems for a moderately subcritical branching process in a random environment
• A unifying approach to branching processes in a varying environment
• Discrete Time Branching Processes in Random Environment
• On Branching Processes in Random Environments
• On Branching Processes with Random Environments: I: Extinction Probabilities
• Branching Processes with Random Environments, II: Limit Theorems