Markov chains with stationary transition probabilities [electronic resource]
From the reviews: J. Neveu, 1962 in Zentralblatt fr Mathematik, 92. Band Heft 2, p. 343: "Ce livre crit par l'un des plus minents spcialistes en la matire, est un expos trs dtaill de la thorie des processus de Markov dfinis sur un espace dnombrable d'tats et homognes dans le temps (ch...
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Full Text (via Springer) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer,
1967.
|
| Edition: | 2d ed. |
| Series: | Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete ;
Bd. 104. |
| Subjects: |
Table of Contents:
- I. Discrete Parameter
- § 1. Fundamental definitions
- § 2. Transition probabilities
- § 3. Classification of states
- § 4. Recurrence
- § 5. Criteria and examples
- § 6. The main limit theorem
- § 7. Various complements
- § 8. Repetitive pattern and renewal process
- § 9. Taboo probabilities
- § 10. The generating function
- § 11. The moments of first entrance time distributions
- § 12. A random walk example
- § 13. System theorems
- § 14. Functionals and associated random variables
- § 15. Ergodic theorems
- § 16. Further limit theorems
- § 17. Almost closed and sojourn sets
- II. Continuous Parameter
- § 1. Transition matrix: basic properties
- § 2. Standard transition matrix
- § 3. Differentiability
- § 4. Definitions and measure-theoretic foundations
- § 5. The sets of constancy
- § 6. Continuity properties of sample functions
- § 7. Further specifications of the process
- § 8. Optional random variable
- § 9. Strong Markov property
- § 10. Classification of states
- § 11. Taboo probability functions
- § 12. Last exit time
- § 13. Ratio limit theorems; discrete approximations
- § 14. Functionals
- § 15. Post-exit process
- § 16. Imbedded renewal process
- § 17. The two systems of differential equations
- § 18. The minimal solution
- § 19. The first infinity
- § 20. Examples.