Markov Chains

Inhaltsverzeichnis

• 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.