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- DescriptionThe 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 phemena. 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 smallersubsetsofstatesprovidessimplerdescriptionsoncyclesthanthe stochastic matrices involved in the taboo probabilities. Also, the rec- rencecriteriaon cyclesimprovepreviousconditionsbased on thestochastic matrices, and provide plenty of examples.
- Author(s)Sophia L. Kalpazidou
- PublisherSpringer-Verlag New York Inc.
- Date of Publication24/05/2006
- Series TitleStochastic Modelling and Applied Probability
- Series Part/Volume Numberv.28
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Note17 black & white illustrations, biography
- Weight1390 g
- Width156 mm
- Height234 mm
- Spine19 mm
- Format DetailsLaminated cover
- Edition Statement2nd ed. 2006
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