ON THE ALMOST SURE CONVERGENCE OF SERIES OF STATIONARY AND RELATED NONSTATIONARY VARIABLES

• 成果类型: Article
• 署名作者: HOUDRE, C
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176988180
• 发表日期: 1995
• 页码: 1204-1218
• 关键词: sequences

摘要

Let (X(n)) be, for example, a weakly stationary sequence or a lacunary system with finite pth moment, 1 less than or equal to p less than or equal to 2, and let {a(n)} be a sequence of scalars. We obtain here conditions which ensure the almost sure convergence of the series Sigma a(n)X(n). When {X(n)} is an orthonormal sequence, the classical Rademacher-Menchov theorem is recovered. This is then applied to study the strong consistency of least squares estimates in multiple regression models.