Strong invariance principles for dependent random variables

• 成果类型: Article
• 署名作者: Wu, Wei Biao
• 署名单位: University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000060
• 发表日期: 2007
• 页码: 2294-2320
• 关键词: CENTRAL-LIMIT-THEOREM; iterated random functions; stationary-processes; partial-sums; approximation theorems; moment inequalities; maximal inequality; mixing sequences; linear-processes; strong laws

摘要

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions.