Moments, moderate and large deviations for a branching process in a random environment

DOI10.1016/j.spa.2011.09.001zbMath1242.60087arXiv1007.1738OpenAlexW2084641710MaRDI QIDQ665437

Chunmao Huang, Quan-sheng Liu

Publication date: 5 March 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.1738

zbMATH Keywords

momentslarge deviationcentral limit theorembranching processrandom environmentmoderate deviationharmonic moments

Mathematics Subject Classification ID

Large deviations (60F10) Processes in random environments (60K37) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• Central limit theorems for a supercritical branching process in a random environment
• A necessary and sufficient condition for a branching process in a random environment to grow like the product of its means
• Limit theorems for branching processes in a random environment
• Harmonic moments and large deviation rates for supercritical branching processes
• Limit theorems for Mandelbrot's multiplicative cascades.
• Asymptotic properties of supercritical age-dependent branching processes and homogeneous branching random walks
• Asymptotic properties and absolute continuity of laws stable by random weighted mean.
• Criticality for branching processes in random environment
• Functional limit theorems for strongly subcritical branching processes in random environment
• Upper large deviations of branching processes in a random environment-offspring distributions with geometrically bounded tails
• Propriétés asymptotiques des processus de branchement en environnement aléatoire
• Branching processes in random environment which extinct at a given moment
• On the limiting distribution of a supercritical branching process in a random environment
• Galton-Watson processes in varying environments
• Large deviations for Branching Processes in Random Environment
• On large deviations of branching processes in a random environment: geometric distribution of descendants
• On Branching Processes in Random Environments
• An invariance principle and some convergence rate results for branching processes
• On Branching Processes with Random Environments: I: Extinction Probabilities
• Local dimensions of the branching measure on a Galton-Watson tree

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