Cycle Representations of Markov Processes [electronic resource] /
Kalpazidou, Sophia L.author.
Provides fresh insight into Markovian dependence via the cycle decompositions. This book presents an account of a class of stochastic processes known as cycle processes. It reveals interpretations of cycle representations such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures.
Description based upon print version of record.
Provides fresh insight into Markovian dependence via the cycle decompositions. This book presents an account of a class of stochastic processes known as cycle processes. It reveals interpretations of cycle representations such as homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures.
Includes bibliographical references (p. [267]-296) and index.
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.
Probabilities.
Probability Theory and Stochastic Processes.
Stochastic modelling and applied probability