Large deviations for sums indexed by the generations of a Galton-Watson process

DOI10.1007/s00440-007-0090-1zbMath1141.60048arXivmath/0605617OpenAlexW2008346699MaRDI QIDQ929373

Vitali Wachtel, Klaus Fleischmann

Publication date: 17 June 2008

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605617

zbMATH Keywords

Böttcher caseSchröder caseLotka-Nagaev estimatorLarge deviation probabilitiesLower deviation probabilitiesSupercritical Galton-Watson processes

Mathematics Subject Classification ID

Large deviations (60F10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (11)

Large deviation for supercritical branching processes with immigration ⋮ Moments and large deviations for supercritical branching processes with immigration in random environments ⋮ On large-deviation probabilities for the empirical distribution of branching random walks with heavy tails ⋮ Deviation estimations for Lotka-Nagaev estimator of a branching process with immigration ⋮ Asymptotic distributions and Berry-Esseen inequalities for Lotka-Nagaev estimator of a Poisson randomly indexed branching process ⋮ Lindeberg's method for moderate deviations and random summation ⋮ Harmonic moments and large deviations for a critical Galton-Watson process with immigration ⋮ On large deviation probabilities for empirical distribution of supercritical branching random walks with unbounded displacements ⋮ Lower deviation and moderate deviation probabilities for maximum of a branching random walk ⋮ Limit theorems for a supercritical Poisson random indexed branching process ⋮ Cramér moderate deviations for a supercritical Galton-Watson process

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