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.
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.
'This excellent textbook by L. Breiman, which was used by many people to learn probability and which was out of print for some years, is again available as an unchanged republication. It gives an introduction to probability based on measure theory.' F. Hofbauer, Monatschefte fur Mathematik 'A reprint of the 1986 Addison-Wesley text, long out of print (TR, October 1968). This is one of the true classics in the field of probability and its reappearance is welcome. At this price it belongs on the shelf of every student and professional in the area.' American Mathematical Monthly 'The style of writing is very informal and chatty. With a few exceptions this goes over quite well. Though one might reproach the author with an undue haste in keeping the reader's attention, and in skimming the cream of many subjects, the overall effect is good and may to some extent alleviate the discouragement of many non-specialists who want a reasonably modern account not overly encumbered with heavy analytic and set-theoretic preliminaries.' D. A. Darling, Mathematical Reviews 'This book is written on an advanced graduate level and addresses statisticians, engineers, and mathematicians who are interested in probability theory and measure and function theory.' Ion A. Craciun, Recenzii
