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Cycle Representations of Markov Processes
ISBN-13:
9781475739299
Veröffentl:
2013
Seiten:
194
Autor:
Sophia L. Kalpazidou
Serie:
28, Stochastic Modelling and Applied Probability
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
I Fundamentals of the Cycle Representations of Markov Processes.- 1 Directed Circuits.- 2 Genesis of Markov Chains by Circuits: The Circuit Chains.- 3 Cycle Representations of Recurrent Denumerable Markov Chains.- 4 Circuit Representations of Finite Recurrent Markov Chains.- 5 Continuous Parameter Circuit Processes with Finite State Space.- 6 Spectral Theory of Circuit Processes.- 7 Higher-Order Circuit Processes.- II Applications of the Cycle Representations.- 1 Stochastic Properties in Terms of Circuits.- 2 Lévy's Theorem Concerning Positiveness of Transition Probabilities.- 3 The Rotational Theory of Markov Processes.- List of Notations.
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