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Resolving Markov Chains onto Bernoulli Shifts via Positive Polynomials
Brian MarcusSelim Tuncel
出版American Mathematical Soc., 2001
主題Biography & Autobiography / Science & TechnologyMathematics / CalculusMathematics / Number TheoryMathematics / Probability & Statistics / GeneralMathematics / Probability & Statistics / Stochastic Processes
ISBN08218264689780821826461
URLhttp://books.google.com.hk/books?id=jJHUCQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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