Entropy of Hidden Markov Processes and Connections to Dynamical Systems
Papers from the Banff International Research Station Workshop
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Entropy of Hidden Markov Processes and Connections to Dynamical Systems
Papers from the Banff International Research Station Workshop
About this book
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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Table of contents
- Cover
- Series-title
- Title
- Copyright
- Contents
- Introduction
- 1 Hidden Markov processes in the context of symbolic dynamics
- 2 On the preservation of Gibbsianness under symbol amalgamation
- 3 A note on a complex Hilbert metric with application to domain of analyticity for entropy rate of hidden Markov processes
- 4 Bounds on the entropy rate of binary hidden Markov processes
- 5 Entropy rate for hidden Markov chains with rare transitions
- 6 The capacity of finite-state channels in the high-noise regime
- 7 Computing entropy rates for hidden Markov processes
- 8 Factors of Gibbs measures for full shifts
- 9 Thermodynamics of hidden Markov processes