Cycle Representations of Markov Processes

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

8. Cycloid Markov Processes

9. Markov Processes on Banach Spaces on Cycles

10. The Cycle Measures

11. Wide-Ranging Interpretations of the Cycle Representations of Markov Processes

II. Applications of the Cycle Representations

12. Stochastic Properties in Terms of Circuits

13. Lévy’s Theorem Concerning Positiveness of Transition Probabilities

14. The Rotational Theory of Markov Processes

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Avainsanat: MATHEMATICS / General MAT000000