On analytic properties of entropy rate

Schönhuth, Alexander (2006) On analytic properties of entropy rate.
Technical Report , 10 p.

Abstract

Entropy rate of discrete random sources are a real valued functional on the space of probability measures associated with the random sources. If one equips this space with a topology one can ask for the analytic properties of the entropy rates. A natural choice is the topology, which is induced by the norm of total variation. A central result is that entropy rate is Lipschitz continuous relative to this topology. The consequences are manifold. First, corollaries are obtained that refer to prevalent objects of probability theory. Second, the result is extended to entropy rate of dynamical systems. Third, it is shown how to exploit the proof schemes to give a direct and elementary proof for the existence of entropy rate of asymptotically mean stationary random sources.


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Item Type: Paper (Technical Report)
Citations: No citation data.
Uncontrolled Keywords: Entropy rate analytic properties discrete random sources dynamical systems
Subjects:
  • 94-XX Information and communication, circuits > 94Axx Communication, information > 94A15 Information theory, general

  • 37-XX Dynamical systems and ergodic theory > 37Axx Ergodic theory > 37A35 Entropy and other invariants, isomorphism, classification

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    Divisions: Institute of Computer Science > Computer Science Department - Prof. Dr. Schrader
    Mathematical Institute > Prof. Dr. Faigle
    Additional Information: modified short version submitted to IEEE Transactions on Information Theory
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    Deposit Information:
    ZAIK Number: zaik2008-568
    Depositing User: Alexander Schönhuth
    Date Deposited: 07 Jan 2008 00:00
    Last Modified: 19 Dec 2011 09:44
    URI: http://e-archive.informatik.uni-koeln.de/id/eprint/568