On the boundary at infinity for branching random walk

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2023-01-01 DOI:10.1214/23-ecp560

Elisabetta Candellero, Tom Hutchcroft

引用次数: 1

Abstract

We prove that a supercritical branching random walk on a transient Markov chain converges almost surely under rescaling to a random measure on the Martin boundary of the underlying Markov chain. Several open problems and conjectures about this limiting measure are presented.

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在无穷远处的分支随机游走的边界上

我们证明了瞬态马尔可夫链上的超临界分支随机游走，在重新标度为底层马尔可夫链的马丁边界上的随机测度时，几乎肯定收敛。对这一极限测度提出了若干有待解决的问题和猜想。

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

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.