Foundations of modern probability/
Olav Kallenberg
- 2nd ed.
- New York: Springer, 2002.
- xvii, 638 p. : ill. ; 24 cm.
- (Probability and its applications) .
1. Measure Theory -- Basic Notions -- 2. Measure Theory -- Key Results -- 3. Processes, Distributions, and Independence -- 4. Random Sequences, Series, and Averages -- 5. Characteristic Functions and Classical Limit Theorems -- 6. Conditioning and Disintegration -- 7. Martingales and Optional Times -- 8. Markov Processes and Discrete-Time Chains -- 9. Random Walks and Renewal Theory -- 10. Stationary Processes and Ergodic Theory -- 11. Special Notions of Symmetry and Invariance -- 12. Poisson and Pure Jump-Type Markov Processes -- 13. Gaussian Processes and Brownian Motion -- 14. Skorohod Embedding and Invariance Principles -- 15. Independent Increments and Infinite Divisibility.