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Cycle Representations of Markov Processes (Hardcover)

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The cycle representations of Markov processes have been advanced after the publication of the ?rst edition to many directions. One main purpose of these advances was the revelation of wide-ranging interpretations of the - cle decompositions of Markov processes such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, disinteg- tions of measures, and so on, which altogether express a genuine law of real phenomena. The versatility of these interpretations is consequently motivated by the existence of algebraic?topological principles in the fundamentals of the - clerepresentationsofMarkovprocesses,whicheliberatesthestandardview on the Markovian modelling to new intuitive and constructive approaches. For instance, the ruling role of the cycles to partition the ?nite-dimensional distributions of certain Markov processes updates Poincare?s spirit to - scribing randomness in terms of the discrete partitions of the dynamical phase state; also, it allows the translation of the famous Minty?s painting lemma (1966) in terms of the stochastic entities. Furthermore, the methods based on the cycle formula of Markov p- cesses are often characterized by minimal descriptions on cycles, which widelyexpressaphilosophicalanalogytotheKolmogoroveanentropicc- plexity. For instance, a deeper scrutiny on the induced Markov chains into smallersubsetsofstatesprovidessimplerdescriptionsoncyclesthanonthe stochastic matrices involved in the ?taboo probabilities. ? Also, the rec- rencecriteriaon cyclesimprovepreviousconditionsbased on thestochastic matrices, and provide plenty of examples.


Publisher Springer Verlag
Mfg Part# 9780387291666
SKU 202573507
Format Hardcover
ISBN10 0387291660
Release Date 4/30/2007
Product Attributes
Book Format Hardcover
Edition 0002
Number of Pages 0301
Publisher Springer
Series Part 28
$219.43 + $2.75 shipping
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