Asymptotic Mean Stationarity of Sources With Finite Evolution Dimension

Faigle, Ulrich and Schönhuth, Alexander (2007) Asymptotic Mean Stationarity of Sources With Finite Evolution Dimension.
Published in: IEEE Transactions on Information Theory Vol. 53 (7). pp. 2342-2348.

Abstract

The notion of the emph{evolution} of a discrete random source with finite alphabet is introduced and its behavior under the action of an associated linear emph{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.


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Deposit Information:
ZAIK Number: zaik2005-498
Depositing User: Prof. Dr. Ulrich Faigle
Date Deposited: 18 Apr 2008 00:00
Last Modified: 09 Jan 2012 16:56
URI: http://e-archive.informatik.uni-koeln.de/id/eprint/498