A second order asymptotic expansion in the local limit theorem for a simple branching random walk in Z(d)

作者：Gao, Zhi-Qiang^*

来源：Stochastic Processes and Their Applications, 2018, 128(12): 4000-4017.

DOI：10.1016/j.spa.2018.01.005

• Branching random walk
• Local limit theorems
• Second-order expansion

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 Z(d). Denote by Z(n) (z) the number of particles of generation n located at site z is an element of Z(d). We give the second order asymptotic expansion for Z(n) (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 Z(d), which is used in the proof of the main theorem and is of independent interest.

• 出版日期2018-12
• 单位北京师范大学