REFINEMENTS IN ASYMPTOTIC EXPANSIONS FOR SUMS OF WEAKLY DEPENDENT RANDOM VECTORS

• 成果类型: Article
• 署名作者: LAHIRI, SN
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989267
• 发表日期: 1993
• 页码: 791-799
• 关键词: markov-chains

摘要

Let S(n) denote the nth normalized partial sum of a sequence of mean zero, weakly dependent random vectors. This paper gives asymptotic expansions for Ef(S(n)) under weaker moment conditions than those of Gotze and Hipp (1983). It is also shown that an expansion for Ef(S(n)) with an error term o(n-(s-2)/2) is valid without any Cramer-type condition, if f has partial derivatives of order (s-1) only. This settles a conjecture of Gotze and Hipp in their 1983 paper.