POLY-ADIC FILTRATIONS, STANDARDNESS, COMPLEMENTABILITY AND MAXIMALITY
成果类型：
Article
署名作者：
Leuridan, Christophe
署名单位：
Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/15-AOP1085
发表日期：
2017
页码：
1218-1246
关键词：
摘要：
Given some essentially separable filtration (Zn)(n <= 0) indexed by the non-positive integers, we define the notion of complementability for the filtrations contained in (Zn)(n <= 0). We also define and characterize the notion ofmaximality for the poly-adic sub-filtrations of (Zn)(n <= 0). We show that any poly-adic sub-filtration of (Zn)(n <= 0) which can be complemented by a Kolmogorovian filtration is maximal in (Zn)(n <= 0). We show that the converse is false, and we prove a partial converse, which generalizes Vershik's lacunary isomorphism theorem for poly-adic filtrations.