1. Introduction; 2. Mathematical framework; 3. Independence; 4. Conditional probability and conditional expectation; 5. Martingales; 6. Stationary processes and the ergodic theorem; 7. Markov chains; 8. Convergence in distribution and the tools thereof; 9. The one-dimensional central limit problem; 10. The renewal theorem and local limit theorem; 11. Multidimensional central limit theorem and Gaussian processes; 12. Stochastic processes and Brownian motion; 13. Invariance theorems; 14. Martingales and processes with stationary, independent increments; 15. Markov processes, introduction and pure jump case; 16. Diffusions; Appendix; Bibliography; Index.
Well known for the clear nature of its exposition, this reprint volume is an excellent introduction to mathematical probability theory.
'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
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