Exact convergence rate of the local limit theorem for branching random walks on the integer lattice

DOI10.1016/j.spa.2016.07.015zbMath1358.60041OpenAlexW2517349456MaRDI QIDQ516017

Zhi-Qiang Gao

Publication date: 20 March 2017

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

Full work available at URL: https://doi.org/10.1016/j.spa.2016.07.015

zbMATH Keywords

local limit theoremsbranching random walkexact convergence rate

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (9)

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 \(\mathbb{Z}^d\) ⋮ Exact convergence rates for particle distributions in a non-lattice branching random walk ⋮ On large deviation probabilities for empirical distribution of supercritical branching random walks with unbounded displacements ⋮ Unnamed Item ⋮ 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 \(\mathbb{Z}^d\) ⋮ Heavy-tailed branching random walks on multidimensional lattices. A moment approach ⋮ 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Almost sure central limit theorem for branching random walks in random environment
• Exact convergence rates in central limit theorems for a branching random walk with a random environment in time
• The central limit theorem for the supercritical branching random walk, and related results
• Central limit theorem for branching random walks in random environment
• Branching random walks. I
• Branching random walks. II
• Convergence rates for branching processes
• Exact convergence rates for the distribution of particles in branching random walks
• Distribution of levels in high-dimensional random landscapes
• Central limit theorems for a branching random walk with a random environment in time
• Random variables, trees, and branching random walks
• Random Walk: A Modern Introduction
• Branching random walk in varying environments
• Asymptotic properties of supercritical branching processes I: The Galton-Watson process
• Large-time asymptotics for the density of a branching Wiener process
• On a conjecture by Harris

This page was built for publication: Exact convergence rate of the local limit theorem for branching random walks on the integer lattice