Entropy of Hidden Markov Processes and Connections to Dynamical Systems (eBook, PDF)

Papers from the Banff International Research Station Workshop
Redaktion: Marcus, Brian

• Format: PDF

Produktbeschreibung

Hidden Markov processes (HMPs) are important objects of study in many areas of pure and applied mathematics, including information theory, probability theory, dynamical systems and statistical physics, with applications in electrical engineering, computer science and molecular biology. This collection of research and survey papers presents important new results and open problems, serving as a unifying gateway for researchers in these areas. Based on talks given at the Banff International Research Station Workshop, 2007, this volume addresses a central problem of the subject: computation of the Shannon entropy rate of an HMP. This is a key quantity in statistical physics and information theory, characterising the fundamental limit on compression and closely related to channel capacity, the limit on reliable communication. Also discussed, from a symbolic dynamics and thermodynamical viewpoint, is the problem of characterizing the mappings between dynamical systems which map Markov measures to Markov (or Gibbs) measures, and which allow for Markov lifts of Markov chains.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 26. Mai 2011
• Englisch
• ISBN-13: 9781139089050
• Artikelnr.: 38268596

Inhaltsangabe

1. Hidden Markov processes in the context of symbolic dynamics Mark Boyle
and Karl Petersen; 2. On the preservation of Gibbsianess under symbol
amalgamation Jean-René Chazottes and E. Ugalde; 3. A note on a complex
Hilbert metric with application to domain of analyticity for entropy rate
of hidden Markov processes Guangyue Han, Brian Marcus and Yuval Peres; 4.
Bounds on the entropy rate of binary hidden Markov processes Erik
Ordentlich and Tsachy Weissman; 5. Entropy rate for hidden Markov chains
with rare transitions Yuval Peres and Anthony Quas; 6. The capacity of
finite-state channels in the high-noise regime Henry Pfister; 7. Computing
entropy rates for hidden Markov processes Mark Pollicott; 8. Factors of
Gibbs measures for full shifts Mark Pollicott and Thomas Kempton; 9.
Thermodynamics of hidden Markov processes Evgeny Verbitskiy.