NONLINEAR RENEWAL THEORY FOR CONDITIONAL RANDOM-WALKS

• 成果类型: Article
• 署名作者: HU, IC
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990553
• 发表日期: 1991
• 页码: 401-422
• 关键词: boundary crossing probabilities; likelihood ratio tests; change-point problems

摘要

Herein boundary crossing behavior of conditional random walks is studied. Asymptotic distributions of the exit time and the excess over the boundary are derived. In the course of derivation, two results of independent interest are also obtained: Lemma 4.1 shows that a conditional random walk behaves like an unconditional one locally in a very strong sense. Theorem B.1 describes a class of distributions over which the renewal theorem holds uniformly. Applications are given for modified repeated significance tests and change-point problems.