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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...

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Bibliographic Details
Main Authors: Bhattacharya, Rabi, Waymire, Edward C. (Author)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2022, 2022
Edition:1st ed. 2022
Series:Graduate Texts in Mathematics
Subjects:
Distribution Theory
Probability Theory
Markov Processes
Stochastic Processes
Markov Process
Distribution (probability Theory)
Probabilities
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

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