On the maximal displacement of subcritical branching random walks

• 成果类型: Article
• 署名作者: Neuman, Eyal; Zheng, Xinghua
• 署名单位: University of Rochester; Hong Kong University of Science & Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0702-8
• 发表日期: 2017
• 页码: 1137-1164
• 关键词: minimal position; brownian-motion; CONVERGENCE; dimensions; time

摘要

We study the maximal displacement of a one dimensional subcritical branching random walk initiated by a single particle at the origin. For each let be the rightmost position reached by the branching random walk up to generation n. Under the assumption that the offspring distribution has a finite third moment and the jump distribution has mean zero and a finite probability generating function, we show that there exists such that the function