Cycle Representations of Markov Processes

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.