Limit theorems for mixing sequences without rate assumptions

• 成果类型: Article
• 署名作者: Berkes, I; Philipp, W
• 署名单位: Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 805-831
• 关键词: random-variables

摘要

We extend Levy's classical criterion for a sequence of independent identically distributed random variables to belong to the domain of partial attraction of a nondegenerate Gaussian law to stationary phi-mixing sequences. We also extend some results of Kesten and of Kuelbs and Zinn on the LIL behavior of independent identically distributed random variables to stationary phi-mixing sequences. No assumptions on the rate of decay for the mixing coefficient are made.