Null flows, positive flows and the structure of stationary symmetric stable processes

• 成果类型: Article
• 署名作者: Samorodnitsky, G
• 署名单位: Cornell University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000305
• 发表日期: 2005
• 页码: 1782-1803
• 关键词: ergodic properties

摘要

This paper elucidates the connection between stationary symmetric alpha-stable processes with 0 < alpha < 2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.