Variable-Length Coding of Two-sided Asymptotically Mean Stationary Measures

被引：7
|
作者：
Debowski, Lukasz [1 ]
机构：
[1] Ctr Wiskunde & Informat, NL-1098 XG Amsterdam, Netherlands
来源：
JOURNAL OF THEORETICAL PROBABILITY | 2010年 / 23卷 / 01期
关键词：
Asymptotically mean stationary processes; Variable-length coding; Synchronization; Shift-invariant algebras; Complete fix-free sets; Finite-energy processes; Block entropy;
D O I：
10.1007/s10959-009-0264-0
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We collect several observations that concern variable-length coding of two-sided infinite sequences in a probabilistic setting. Attention is paid to images and preimages of asymptotically mean stationary measures defined on subsets of these sequences. We point out sufficient conditions under which the variable-length coding and its inverse preserve asymptotic mean stationarity. Moreover, conditions for preservation of shift-invariant sigma-fields and the finite-energy property are discussed, and the block entropies for stationary means of coded processes are related in some cases. Subsequently, we apply certain of these results to construct a stationary nonergodic process with a desired linguistic interpretation.
引用
收藏
页码：237 / 256
页数：20
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