A UNIFORM CENTRAL-LIMIT-THEOREM FOR NONUNIFORM PHI-MIXING RANDOM-FIELDS

• 成果类型: Article
• 署名作者: CHEN, DC
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990445
• 发表日期: 1991
• 页码: 636-649
• 关键词: partial-sum processes; finite variance; CONVERGENCE

摘要

A sufficient condition is given for a sequence of partial-sum set-indexed processes with nonuniform phi-mixing condition to converge to Brownian motion. The main result (Theorem 1.1) is an extension of the similar results of Goldie and Greenwood by weakening the phi-mixing condition. An application (Corollary 4.2) to certain Gibbs fields is given.