Sufficient conditions for the filtration of a stationary processes to be standard
成果类型：
Article
署名作者：
Ceillier, Gael; Leuridan, Christophe
署名单位：
Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-016-0696-2
发表日期：
2017
页码：
979-999
关键词：
摘要：
Let X be a stationary process with values in some -finite measured state space , indexed by . Call its natural filtration. In Ceillier (Ann Probab 40(5):1980-2007, 2012), sufficient conditions were given for to be standard when E is finite, and the proof used a coupling of all probabilities on the finite set E. In this paper, we construct a coupling of all laws having a density with regard to , which is much more involved. Then, we provide sufficient conditions for to be standard, generalizing those in Ceillier (Ann Probab 40(5):1980-2007, 2012).