Cycle Representations of Markov Processes

Sophia L. Kalpazidou (Autor)

Buch | Softcover

304 Seiten

2010 | Softcover reprint of hardcover 2nd ed. 2006
Springer-Verlag New York Inc.
978-1-4419-2121-5 (ISBN)

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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.

Fundamentals of the Cycle Representations of Markov Processes.- Directed Circuits.- Genesis of Markov Chains by Circuits: The Circuit Chains.- Cycle Representations of Recurrent Denumerable Markov Chains.- Circuit Representations of Finite Recurrent Markov Chains.- Continuous Parameter Circuit Processes with Finite State Space.- Spectral Theory of Circuit Processes.- Higher-Order Circuit Processes.- Cycloid Markov Processes.- Markov Processes on Banach Spaces on Cycles.- The Cycle Measures.- Wide-Ranging Interpretations of the Cycle Representations of Markov Processes.- Applications of the Cycle Representations.- Stochastic Properties in Terms of Circuits.- Lévy’s Theorem Concerning Positiveness of Transition Probabilities.- The Rotational Theory of Markov Processes.

Erscheint lt. Verlag	23.11.2010
Reihe/Serie	Stochastic Modelling and Applied Probability ; 28
Zusatzinfo	17 Illustrations, black and white; XX, 304 p. 17 illus.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	1-4419-2121-4 / 1441921214
ISBN-13	978-1-4419-2121-5 / 9781441921215
Zustand	Neuware