Stationary Processes and Discrete Parameter Markov Processes
This textbook explores two distinct stochastic processes that evolve at random: weakly stationary processes and discrete parameter Markov processes. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approac...
Main Authors: | , |
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Format: | eBook |
Language: | English |
Published: |
Cham
Springer International Publishing
2022, 2022
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Edition: | 1st ed. 2022 |
Series: | Graduate Texts in Mathematics
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Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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