FIRST-PASSAGE TIMES FOR RANDOM WALKS WITH NONIDENTICALLY DISTRIBUTED INCREMENTS

• 成果类型: Article
• 署名作者: Denisov, Denis; Sakhanenko, Alexander; Wachtel, Vitali
• 署名单位: University of Manchester; Nankai University; University of Augsburg
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/17-AOP1248
• 发表日期: 2018
• 页码: 3313-3350
• 关键词: limit-theorems; invariance-principle; BOUNDARY; CONVERGENCE; variables; stay; EXIT

摘要

We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first passage times over moving boundaries. Furthermore, we prove that a properly rescaled random walk conditioned to stay above the boundary up to time n converges, as n -> infinity towards the Brownian meander.