VARIANCE OF PARTIAL SUMS OF STATIONARY SEQUENCES

• 成果类型: Article
• 署名作者: Deligiannidis, George; Utev, Sergey
• 署名单位: University of Oxford; University of Nottingham
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP772
• 发表日期: 2013
• 页码: 3606-3616
• 关键词: limit-theorems

摘要

Let X-1, X-2, ... be a centred sequence of weakly stationary random variables with spectral measure F and partial sums S-n = X-1 + ... + X-n. We show that var(S-n) is regularly varying of index gamma at infinity, if and only if G(x) := integral(x)(-x) F(dx) is regularly varying of index 2 - gamma at the origin (0 < gamma < 2).