ON 1-DEPENDENT PROCESSES AND K-BLOCK FACTORS
成果类型：
Article
署名作者：
BURTON, RM; GOULET, M; MEESTER, R
署名单位：
Utrecht University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989014
发表日期：
1993
页码：
2157-2168
关键词：
摘要：
A stationary process {X(n)}(n epsilon Z) is said to be k-dependent if {X(n)}(n<0) is independent of {X(n)}(n>k-1). It is said to be a k-block factor of a process {Y-n} if it can be represented as X(n) = f(Y-n,...,Y-n+k-1), where f is a measurable function of k variables. Any (k + 1)-block factor of an i.i.d. process is k-dependent. We answer an old question by showing that there exists a one-dependent process which is not a k-block factor of any i.i.d. process for any k. Our method also leads to generalizations of this result and to a simple construction of an eight-state one-dependent Markov chain which is not a two-block factor of an i.i.d. process.