Stable stationary processes related to cyclic flows

• 成果类型: Article
• 署名作者: Pipiras, V; Taqqu, MS
• 署名单位: Boston University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000108
• 发表日期: 2004
• 页码: 2222-2260
• 关键词: mixed moving averages; DECOMPOSITION

摘要

We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163-1187]. These processes are not ergodic. We provide their canonical representations, consider examples and show how to identify them among general stationary stable processes. We conclude with the unique decomposition in distribution of stationary stable processes into the sum of four major independent components: 1. A mixed moving average component. 2. A harmonizable (or trivial) component. 3. A cyclic component 4. A component which is different from these.