Harmonic moments and large deviations for a supercritical branching process in a random environment

DOI10.1016/j.crma.2011.10.001zbMath1231.60119arXiv1608.08075OpenAlexW1980572549MaRDI QIDQ5894401

Chunmao Huang, Quan-sheng Liu, I. G. Grama, Eric Miqueu

Publication date: 7 December 2011

Published in: Electronic Journal of Probability, Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.08075

zbMATH Keywords

branching processesphase transitionscentral limit theoremlarge deviationsrandom environmentharmonic momentslarge and moderate deviation principlessupercritical branching process

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Applications of branching processes (60J85) Population dynamics (general) (92D25) Large deviations (60F10) Processes in random environments (60K37) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (10)

Moments and large deviations for supercritical branching processes with immigration in random environments ⋮ Random walks and branching processes in correlated Gaussian environment ⋮ Asymptotic properties for branching random walks with immigration in random environments ⋮ Small positive values for supercritical branching processes in random environment ⋮ Asymptotics of the distribution and harmonic moments for a supercritical branching process in a random environment ⋮ Non-uniform Berry-Esseen-type inequalities for a supercritical branching process with immigration in a random environment ⋮ Moments, large and moderate deviations for branching random walks with immigration in random environments ⋮ Asymptotic distributions and Berry-Esseen inequalities for Lotka-Nagaev estimator of a Poisson randomly indexed branching process ⋮ Absolute continuity of the martingale limit in branching processes in random environment ⋮ Moments and asymptotic properties for supercritical branching processes with immigration in random environments

Cites Work

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• Limit theorems for branching processes in a random environment
• Harmonic moments and large deviation rates for supercritical branching processes
• Asymptotic properties and absolute continuity of laws stable by random weighted mean.
• Propriétés asymptotiques des processus de branchement en environnement aléatoire
• On the limiting distribution of a supercritical branching process in a random environment
• Large deviations for Branching Processes in Random Environment

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