Resolving Markov Chains onto Bernoulli Shifts via Positive Polynomials

Released on by Brian Marcus
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  • Resolving Markov Chains onto Bernoulli Shifts via Positive Polynomials Book Detail

  • Author : Brian Marcus
  • Release Date : 2001
  • Publisher : American Mathematical Soc.
  • Genre : Biography & Autobiography
  • Pages : 114
  • ISBN 13 : 0821826468
  • File Size : 97,97 MB
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Resolving Markov Chains onto Bernoulli Shifts via Positive Polynomials by Brian Marcus PDF Summary

Book Description: The two parts of this monograph contain two separate but related papers. The longer paper in Part A obtains necessary and sufficient conditions for several types of codings of Markov chains onto Bernoulli shifts. It proceeds by replacing the defining stochastic matrix of each Markov chain by a matrix whose entries are polynomials with positive coefficients in several variables; a Bernoulli shift is represented by a single polynomial with positive coefficients, $p$. This transforms jointly topological and measure-theoretic coding problems into combinatorial ones. In solving the combinatorial problems in Part A, the work states and makes use of facts from Part B concerning $p DEGREESn$ and its coefficients. Part B contains the shorter paper on $p DEGREESn$ and its coefficients, and is independ

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