Probability - Breiman, Leo 1928-2005 (Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1992)
Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader
Includes bibliographical references (p. 405-411) and index
Chapter 1. Introduction -- Chapter 2. Mathematical framework -- Chapter 3. Independence -- Chapter 4. Conditional probability and conditional expectation -- Chapter 5. Martingales -- Chapter 6. Stationary processes and the Ergodic theorem -- Chapter 7. Markov chains -- Chapter 8. Convergence in distribution and the tools thereof -- Chapter 9. The one-dimensional central limit problem -- Chapter 10. The renewal theorem and local limit theorem -- Chapter 11. Multidimensional central limit theorem and Gaussian processes -- Chapter 12. Stochastic processes and Brownian motion -- Chapter 13. Invariance theorems -- Chapter 14. Martingales and processes with stationary, independent increments -- Chapter 15. Markov processes, introduction and pure jump case -- Chapter 16. Diffusions -- Appendix. On measure and function theory -- Bibliography -- Index
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. Designed around the needs of the student, this book achieves readability and clarity by giving the most important results in each area while not dwelling on any one subject. Each new idea or concept is introduced from an intuitive, common-sense point of view. Students are helped to understand why things work, instead of being given a dry theorem-proof regime