Asymptotic Mean Stationarity of Sources With Finite Evolution Dimension

Author

Faigle, Ulrich ; Schönhuth, Alexander

Author_Institution

Univ. Cologne, Cologne

Volume

53

Issue

7

fYear

2007

fDate

7/1/2007 12:00:00 AM

Firstpage

2342

Lastpage

2348

Abstract

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.

Keywords

entropy; hidden Markov models; random processes; Markov sources; associated linear evolution operator; asymptotic mean stationarity; discrete random source; ergodic properties; finitary stochastic processes; finite alphabet; finite evolution dimension; stable dynamical systems; well-defined entropy rate; Computer science; Concrete; Data analysis; Entropy; Hidden Markov models; Indium tin oxide; Linear algebra; Sampling methods; Stochastic processes; Terminology; Asymptotic mean; Markov chain; dimension; entropy; ergodic; evolution operator; hidden Markov model (HMM); linearly dependent process; observable operator model; random source; stable; state generating function; stationary;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2007.899514

Filename

4252328