A strong invariance principle for associated random fields

• 成果类型: Article
• 署名作者: Balan, RM
• 署名单位: University of Ottawa
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000001071
• 发表日期: 2005
• 页码: 823-840
• 关键词: strassen-type laws; iterated logarithm; random-variables; random vectors; functional law; SEQUENCES; inequalities; THEOREMS

摘要

In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097] strong invariance principle for associated sequences to the multi-parameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n -> infinity. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15-37] multiparameter blocking technique, the Csorgo and Revesz [Z. Wahrsch. Verw.. Gebiete 31 (1975) 255-260] quantile transform method and the Bulinski [Theory Probab. Appl. 40 (1995) 136-144] rate of convergence in the CLT.