Cycle Representations of Markov Processes

Sophia L. Kalpazidou (Autor)

Buch | Softcover

304 Seiten

2010 | Second Edition 2006
Springer-Verlag New York Inc.
978-1-4419-2121-5 (ISBN)

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This book provides new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called because they may be defined by directed cycles. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. This expanded second edition adds new advances, which reveal wide-ranging interpretations of cycle representations such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The text includes chapter summaries as well as a number of detailed illustrations.

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
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