A second order asymptotic expansion in the local limit theorem for a simple branching random walk in Zd
Stochastic Processes and their Applications, 2018, vol. 128, issue 12, 4000-4017
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton–Watson process and the migration of particles by a simple random walk in Zd. Denote by Zn(z) the number of particles of generation n located at site z∈Zd. We give the second order asymptotic expansion for Zn(z). The higher order expansion can be derived by using our method here. As a by-product, we give the second order expansion for a simple random walk on Zd, which is used in the proof of the main theorem and is of independent interest.
Keywords: Branching random walk; Local limit theorems; Second-order expansion (search for similar items in EconPapers)
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