A second order asymptotic expansion in the local limit theorem for a simple branching random walk in |
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Authors: | Zhi-Qiang Gao |
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Institution: | Laboratory of Mathematics and Complex Systems (Ministry of Education of China), School of Mathematical Sciences, Beijing Normal University, Beijing 100875, PR China |
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Abstract: | 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 . Denote by the number of particles of generation located at site . We give the second order asymptotic expansion for . 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 , which is used in the proof of the main theorem and is of independent interest. |
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Keywords: | 60F05 60J10 60G50 60J80 Branching random walk Local limit theorems Second-order expansion |
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