Asymptotic mean stationarity of sources with finite evolution dimension

被引：11
|
作者：
Faigle, Ulrich [1 ]
Schoenhuth, Alexander [1 ]
机构：
[1] Univ Cologne, Ctr Appl Comp Sci, Math Inst, D-50931 Cologne, Germany
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2007年 / 53卷 / 07期
关键词：
asymptotic mean; dimension; entropy; ergodic; evolution operator; hidden Markov model (HMM); linearly dependent process; Markov chain; observable operator model; random source; stable; state generating function; stationary;
D O I：
10.1109/TIT.2007.899514
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The notion of the evolution of a discrete random source with finite alphabet is introduced and its behavior under the action of an associated linear evolution operator is studied. Viewing these sources as possibly stable dynamical systems it is proved that all random sources with finite evolution dimension are asymptotically mean stationary, which implies that such random sources have ergodic properties and a well-defined entropy rate. It is shown that the class of random sources with finite evolution dimension properly generalizes the well-studied class of finitary stochastic processes, which includes (hidden) Markov sources as special cases.
引用
收藏
页码：2342 / 2348
页数：7
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