Well known for the clear, inductive nature of its exposition, this reprint volume is an excellent introduction to mathematical probability theory. It may be used as a graduate-level text in one- or two-semester courses in probability for students who are familiar with basic measure theory, or as a supplement in courses in stochastic processes or mathematical statistics.
Well known for the clear, inductive nature of its exposition, this reprint volume is an excellent introduction to mathematical probability theory. It may be used as a graduate-level text in one- or two-semester courses in probability for students who are familiar with basic measure theory, or as a supplement in courses in stochastic processes or mathematical statistics.
1. Chapter 1: Introduction 2. Chapter 2: Mathematical Framework 3. Chapter 3: Independence 4. Chapter 4: Conditional Probability and Conditional Expectation 5. Chapter 5: Martingales 6. Chapter 6: Stationary Processes and the Ergodic Theorem 7. Chapter 7: Markov Chains 8. Chapter 8: Convergence in Distribution and the Tools Thereof 9. Chapter 9: The One-Dimensional Central Limit Problem 10. Chapter 10: The Renewal Theorem and Local Limit Theorem 11. Chapter 11: Multidimensional Central Limit Theorem and Gaussian Processes 12. Chapter 12: Stochastic Processes and Brownian Motion 13. Chapter 13: Invariance Theorems 14. Chapter 14: Martingales and Processes with Stationary, Independent Increments 15. Chapter 15: Markov Processes, Introduction and Pure Jump Case 16. Chapter 16: Diffusions 17. Appendix: On Measure and Function Theory 18. Bibliography 19. Index.
1. Chapter 1: Introduction 2. Chapter 2: Mathematical Framework 3. Chapter 3: Independence 4. Chapter 4: Conditional Probability and Conditional Expectation 5. Chapter 5: Martingales 6. Chapter 6: Stationary Processes and the Ergodic Theorem 7. Chapter 7: Markov Chains 8. Chapter 8: Convergence in Distribution and the Tools Thereof 9. Chapter 9: The One-Dimensional Central Limit Problem 10. Chapter 10: The Renewal Theorem and Local Limit Theorem 11. Chapter 11: Multidimensional Central Limit Theorem and Gaussian Processes 12. Chapter 12: Stochastic Processes and Brownian Motion 13. Chapter 13: Invariance Theorems 14. Chapter 14: Martingales and Processes with Stationary, Independent Increments 15. Chapter 15: Markov Processes, Introduction and Pure Jump Case 16. Chapter 16: Diffusions 17. Appendix: On Measure and Function Theory 18. Bibliography 19. Index.
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