Stationary processes whose filtrations are standard

• 成果类型: Article
• 署名作者: Bressaud, X.; Maass, A.; Martinez, S.; San Martin, J.
• 署名单位: Aix-Marseille Universite; Universidad de Chile
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000151
• 发表日期: 2006
• 页码: 1589-1600
• 关键词: decreasing sequences

摘要

We study the standard property of the natural filtration associated to a 0-1 valued stationary process. In our main result we show that if the process has summable memory decay, then the associated filtration is standard. We prove it by coupling techniques. For a process whose associated filtration is standard, we construct a product type filtration extending it, based upon the usual couplings and the Vershik's criterion for standardness.