Propagation of the Front of Random Walk with Periodic Branching Sources

IF 0.2 Q4 MATHEMATICS

Moscow University Mathematics Bulletin Pub Date : 2024-05-13 DOI:10.3103/s0027132224700049

E. Vl. Bulinskaya

引用次数: 0

Abstract

We consider the model of branching random walk on an integer lattice \(\mathbb{Z}^{d}\) with periodic sources of branching. It is supposed that the regime of branching is supercritical and the Cramér condition is satisfied for a jump of the random walk. The theorem established describes the rate of front propagation for particles population over the lattice as the time increases unboundedly. The proofs are based on fundamental results related to the spatial spread of general branching random walk.

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带有周期性分支源的随机漫步前沿传播

摘要我们考虑了整数网格 \(\mathbb{Z}^{d}\)上具有周期性分支源的分支随机行走模型。我们假定分支机制是超临界的，随机游走的跳跃满足克拉梅尔条件。所建立的定理描述了随着时间的无限制增加，粒子群在网格上的前沿传播速度。证明基于与一般分支随机游走的空间扩散相关的基本结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow University Mathematics Bulletin MATHEMATICS-

CiteScore

0.60

自引率

25.00%

发文量

期刊介绍： Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.