A Course in Probability TheorySince the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication. |
Contents
Chapter 1 Distribution function | 1 |
Chapter 2 Measure theory | 16 |
Chapter 3 Random variable Expectation Independence | 34 |
Chapter 4 Convergence concepts | 68 |
Chapter 5 Law of large numbers Random series | 106 |
Chapter 6 Characteristic function | 150 |
Chapter 7 Central limit theorem and its ramifications | 205 |
Chapter 8 Random walk | 263 |
Chapter 9 Conditioning Markov property Martingale | 310 |
Measure and Integral | 375 |
| 413 | |
| 415 | |
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Common terms and phrases
apply arbitrary assertion Borel field Borel measurable bounded central limit theorem ch.f condition continuous convergence theorem converges a.e. converges in dist Corollary countable countable set defined definition denote dF(x disjoint E(Xn eitx equation equivalent example Exercise exists finite number follows function ƒ given Hence HINT identically distributed r.v.'s implies independent r.v.'s inequality infinitely divisible interval large numbers law of large Lebesgue Lebesgue measure left member lemma Let f Let Xn Markov property martingale notation null set obtain probability space proof of Theorem Prove random walk real numbers replaced result right member S₁ satisfying sequence of independent sequence of r.v.'s submartingale subsets supermartingale Suppose trivial uniformly integrable X₁ zero