依时变化的随机环境中的分枝随机游动的局部极限定理的二阶展开

摘要/Abstract

摘要：

考虑了 ${\mathbb{Z}}^d$ 中随机环境中的分枝随机游动, 其中分枝机制和粒子迁移的分布律均依时间变化.对任意给定点 $z\in{\mathbb{Z}}^d$ , 令 $Z_n (z)$ 表示位于该点处的 $n$ 代粒子的个数.给出了 $Z_n (z)$ 的二阶渐近展开表达式.

关键词: 分枝随机游动, 局部极限定理, 渐近展开

Abstract:

Consider a branching random walk on ${\mathbb{Z}}^d$ with a random environment in time, where the branching offspring distribution and the migration law change as times goes by. Under the mild moment conditions, we derive the second order expansion for $Z_n(z)$ , which counts the number of particles of generation $n$ at $z\in {\mathbb{Z}}^d$ .

Key words: Branching random walk, Local limit theorem, Asymptotic expansions

中图分类号:

O211.6

高志强. 依时变化的随机环境中的分枝随机游动的局部极限定理的二阶展开[J]. 数学物理学报, 2022, 42(1): 282-305.

Zhiqiang Gao. A Second Order Correction of the Local Limit Theorem for a Branching Random Walk with a Random Environment in Time on ${\mathbb{Z}}^d$ [J]. Acta mathematica scientia,Series A, 2022, 42(1): 282-305.

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