目次

Symbol Definition List.- 1. Fourier Analysis: A Brief.- 2. Weakly Stationary Processes and their Spectral Measures.- 3. Spectral Representation of Stationary Processes.- 4. Birkhoff’s Ergodic Theorem.- 5. Subadditive Ergodic Theory.- 6. An Introduction to Dynamical Systems.- 7. Markov Chains.- 8. Markov Processes with General State Space.- 9. Stopping Times and the Strong Markov Property.- 10. Transience and Recurrence of Markov Chains.- 11. Birth–Death Chains.- 12. Hitting Probabilities & Absorption.- 13. Law of Large Numbers and Invariant Probability for Markov Chains by Renewal Decomposition.- 14. The Central Limit Theorem for Markov Chains by Renewal Decomposition.- 15. Martingale Central Limit Theorem.- 16. Stationary Ergodic Markov Processes: SLLN & FCLT.- 17. Linear Markov Processes.- 18. Markov Processes Generated by Iterations of I.I.D. Maps.- 19. A Splitting Condition and Geometric Rates of Convergence to Equilibrium.- 20. Irreducibility and Harris Recurrent Markov Processes.- 21. An Extended Perron–Frobenius Theorem and Large Deviation Theory for Markov Processes.- 22. Special Topic: Applications of Large Deviation Theory.- 23. Special Topic: Associated Random Fields, Positive Dependence, FKG Inequalities.- 24. Special Topic: More on Coupling Methods and Applications.- 25. Special Topic: An Introduction to Kalman Filter.- A. Spectral Theorem for Compact Self-Adjoint Operators and Mercer’s Theorem.- B. Spectral Theorem for Bounded Self-Adjoint Operators.- C. Borel Equivalence for Polish Spaces.- D. Hahn–Banach, Separation, and Representation Theorems in Functional Analysis.- References.- Author Index.- Subject Index.