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

Zhiqiang Gao

Stochastic Processes and their Applications, 2017, vol. 127, issue 4, 1282-1296

Abstract: Consider branching random walks on the integer lattice Zd, where the branching mechanism is governed by a supercritical Galton–Watson process and the particles perform a symmetric nearest-neighbor random walk whose increments equal to zero with probability r∈[0,1). We derive exact convergence rate in the local limit theorem for distributions of particles. When r=0, our results correct and improve the existing results on the convergence speed conjectured by Révész (1994) and proved by Chen (2001). As a byproduct, we obtain exact convergence rate in the local limit theorem for some symmetric nearest-neighbor random walks, which is of independent interest.

Keywords: Branching random walk; Local limit theorems; Exact convergence rate (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:4:p:1282-1296

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DOI: 10.1016/j.spa.2016.07.015

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