Exact convergence rates for the distribution of particles in branching random walks

DOI10.1214/aoap/1015345402zbMath1012.60080OpenAlexW2024802061MaRDI QIDQ1872424

Xia Chen

Publication date: 6 May 2003

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1015345402

zbMATH Keywords

central limit theoremlocal limit theoremsupercritical branching random walksupercritical branching Wiener process

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) (L^p)-limit theorems (60F25)

Related Items (20)

Asymptotic expansions in the central limit theorem for a branching Wiener process ⋮ A second order asymptotic expansion in the local limit theorem for a simple branching random walk in \(\mathbb{Z}^d\) ⋮ A prediction problem of the branching random walk ⋮ On large-deviation probabilities for the empirical distribution of branching random walks with heavy tails ⋮ First- and second-order expansions in the central limit theorem for a branching random walk ⋮ Distribution of levels in high-dimensional random landscapes ⋮ Asymptotic expansions in the local limit theorem for a branching Wiener process ⋮ Edgeworth expansions for profiles of lattice branching random walks ⋮ Berry-Esseen bound and Cramér moderate deviation expansion for a supercritical branching random walk ⋮ General Edgeworth expansions with applications to profiles of random trees ⋮ Moderate deviation probabilities for empirical distribution of the branching random walk ⋮ Exact convergence rates for particle distributions in a non-lattice branching random walk ⋮ Exact convergence rate of the local limit theorem for branching random walks on the integer lattice ⋮ On large deviation probabilities for empirical distribution of supercritical branching random walks with unbounded displacements ⋮ Unnamed Item ⋮ Exact convergence rates in central limit theorems for a branching random walk with a random environment in time ⋮ Large-time asymptotics for the density of a branching Wiener process ⋮ A note on exact convergence rate in the local limit theorem for a lattice branching random walk ⋮ Exact convergence rate in the local central limit theorem for a lattice branching random walk on \(\mathbb{Z}^d\) ⋮ Exact convergence rate of the local limit theorem for a branching random walk in a time-dependent random environment on d-dimensional integer lattice

Cites Work

• The central limit theorem for the supercritical branching random walk, and related results
• The population composition of a multitype branching random walk
• On the branching process for Brownian particles with an absorbing boundary
• Branching random walk in varying environments
• On a conjecture by Harris
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