Language: English
ISBN/ISSN: 7030166728
Published on: 2006-01
Hardcover
Foundations of Modern Probability Second Edition
kallenberg的这本书博采众家之长，内容丰富翔实，论述清晰独到，专注于数学论述，而无丝毫偏离。大胆一阅该书的读者，将会相信他 们有了一位能力出众的舵手。 ——．f．b．knight，数学评论.
该专著绝对有望成为概率论的大多数领域在未来的十年或者更久的一本(甚至可能是“唯一”)主要参考书。——m．scheutzow，zentralblatt
20世纪的下半叶，概率论发展得非常迅猛；试图写一本综合参考书，涵盖现代概率论的大多数领域，看来真的莽撞。然而，kallenberg教授尝试了，并且完成得很漂亮。令人惊讶的是，简简单单的一本书，仅有500来页，却涉及如此之多的论题，阐述得如此严谨，而至少形式上自成体系。——r．k．getoor,melrica..
修订版增加了四章，并对原版内容作了大量修改。
Preface to the Second Edition
Preface to the First Edition
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
16. Convergence of Random Processes, Measures, and Sets
17. Stochastic Integrals and Quadratic Variation
18. Continuous Martingales and Brownian Motion
19. Feller Processes and Semigroups
20. ergodic Properties of Markov Processes
21. Stochastic Differential Equations
22. Local Time, Excursions, and Additive Functionals
23. One-dimensional SDEs and Diffusions
24. Connections with PDEs and Potential Theory
25. Predictability, Compensation, and Excessive Functions
26. Semimartingales and General Stochastic Integration
27. Large Deviations
Appendices
Historical and Bibliographical Notes
Bibliography
Symbol Index
Author Index
Subject Index
