SUFFICIENT CONDITIONS OF STANDARDNESS FOR FILTRATIONS OF STATIONARY PROCESSES TAKING VALUES IN A FINITE SPACE
成果类型：
Article
署名作者：
Ceillier, Gael
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/11-AOP666
发表日期：
2012
页码：
1980-2007
关键词：
摘要：
Let X be a stationary process with finite state-space A. Bressaud et al. [Ann. Probab. 34 (2006) 1589-1600] recently provided a sufficient condition for the natural filtration of X to be standard when A has size 2. Their condition involves the conditional laws p(.vertical bar x) of X-0 conditionally on the whole past (X-k)(k <=-1) = x and controls the strength of the influence of the old past of the process on its present X-0. It involves the maximal gaps between p(.vertical bar x) and p(.vertical bar y) for infinite sequences x and y which coincide on their n last terms. In this paper, we first show that a slightly stronger result holds for any finite state-space. Then, we provide sufficient conditions for standardness based on average gaps instead of maximal gaps.
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