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Inhaltsangabe
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.
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.
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