TY - BOOK AU - Kallenberg, Olav TI - Foundations of modern probability SN - 9780387953137 U1 - 519.2 PY - 2002/// CY - New York PB - Springer KW - Probabilities N1 - 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 ER -