Conditional \(L^1\)-convergence for the martingale of a critical branching process in random environment

DOI10.1134/S0081543822010138OpenAlexW4225150601MaRDI QIDQ2135130

Xiaoyue Zhang, Wenming Hong, Shengli Liang

Publication date: 4 May 2022

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543822010138

zbMATH Keywords

random environmentGalton-Watson processcritical branching processtime-inhomogeneous processassociated random walkconditional limit behaviormartingale convergence in \(L^1\)

Mathematics Subject Classification ID

Processes in random environments (60K37) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Cites Work

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• Time reversal of random walks in one dimension
• Local probabilities for random walks conditioned to stay positive
• A necessary and sufficient condition for a branching process in a random environment to grow like the product of its means
• Change of measures for Markov chains and the \(L\log L\) theorem for branching processes
• Criticality for branching processes in random environment
• Conceptual proofs of \(L\log L\) criteria for mean behavior of branching processes
• 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
• Probability
• Measure change in multitype branching
• Discrete Time Branching Processes in Random Environment
• On Branching Processes in Random Environments
• A Limit Theorem for Multidimensional Galton-Watson Processes
• On Branching Processes with Random Environments: I: Extinction Probabilities
• Branching Processes with Random Environments, II: Limit Theorems

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