Cycle Representations of Markov Processes (Paperback, Softcover reprint of hardcover 2nd ed. 2006)

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.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Stochastic Modelling and Applied Probability, 28
Release date:	November 2010
First published:	2006
Authors:	Sophia L. Kalpazidou
Dimensions:	235 x 155 x 17mm (L x W x T)
Format:	Paperback
Pages:	304
Edition:	Softcover reprint of hardcover 2nd ed. 2006
ISBN-13:	978-1-4419-2121-5
Categories:	Books > Science & Mathematics > Mathematics > Probability & statistics
LSN:	1-4419-2121-4
Barcode:	9781441921215

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