Probability

Leo Breiman9780898712964, 0898712963

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.

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Table of contents :
Probability……Page 1
Preface to the Classic Edition……Page 8
Preface……Page 10
Contents……Page 12
CHAPTER 1 INTRODUCTION……Page 18
CHAPTER 2 MATHEMATICAL FRAMEWORK……Page 36
CHAPTER 3 INDEPENDENCE……Page 53
CHAPTER 4 CONDITIONAL PROBABILITY AND CONDITIONAL EXPECTATION……Page 84
CHAPTER 5 MARTINGALES……Page 99
CHAPTER 6 STATIONARY PROCESSES AND THE ERGODIC THEOREM……Page 121
CHAPTER 7 MARKOV CHAINS……Page 146
CHAPTER 8 CONVERGENCE IN DISTRIBUTION AND THE TOOLS THEREOF……Page 176
CHAPTER 9 THE ONE-DIMENSIONAL CENTRAL LIMIT PROBLEM……Page 202
CHAPTER 10 THE RENEWAL THEOREM AND LOCAL LIMIT THEOREM……Page 233
CHAPTER 11 MULTIDIMENSIONAL CENTRAL LIMIT THEOREM AND GAUSSIAN PROCESSES……Page 250
CHAPTER 12 STOCHASTIC PROCESSES AND BROWNIAN MOTION……Page 265
CHAPTER 13 INVARIANCE THEOREMS……Page 289
CHAPTER 14 MARTINGALES AND PROCESSES WITH STATIONARY, INDEPENDENT INCREMENTS……Page 315
CHAPTER 15 MARKOV PROCESSES,INTRODUCTION AND PURE JUMP CASE……Page 336
CHAPTER 16 DIFFUSIONS……Page 364
APPENDIX ON MEASURE AND FUNCTION THEORY……Page 408
BIBLIOGRAPHY……Page 422
INDEX……Page 429