Probability EssentialsSpringer Science & Business Media, 6 dic 2012 - 254 pagine We have made small changes throughout the book, including the exercises, and we have tried to correct if not all, then at least most of the typos. We wish to thank the many colleagues and students who have commented c- structively on the book since its publication two years ago, and in particular Professors Valentin Petrov, Esko Valkeila, Volker Priebe, and Frank Knight. Jean Jacod, Paris Philip Protter, Ithaca March, 2002 Preface to the Second Printing of the Second Edition We have bene?ted greatly from the long list of typos and small suggestions sent to us by Professor Luis Tenorio. These corrections have improved the book in subtle yet important ways, and the authors are most grateful to him. Jean Jacod, Paris Philip Protter, Ithaca January, 2004 Preface to the First Edition We present here a one semester course on Probability Theory. We also treat measure theory and Lebesgue integration, concentrating on those aspects which are especially germane to the study of Probability Theory. The book is intended to ?ll a current need: there are mathematically sophisticated s- dents and researchers (especially in Engineering, Economics, and Statistics) who need a proper grounding in Probability in order to pursue their primary interests. Many Probability texts available today are celebrations of Pr- ability Theory, containing treatments of fascinating topics to be sure, but nevertheless they make it di?cult to construct a lean one semester course that covers (what we believe) are the essential topics. |
Sommario
| 1 | |
| 6 | |
Conditional Probability and Independence | 15 |
Probabilities on a Finite or Countable Space | 21 |
Random Variables on a Countable Space | 27 |
Construction of a Probability Measure | 35 |
Construction of a Probability Measure on R | 39 |
Random Variables | 47 |
Convergence of Random Variables | 141 |
Weak Convergence 151 | 150 |
Weak Convergence and Characteristic Functions | 167 |
The Laws of Large Numbers | 173 |
The Central Limit Theorem 181 | 180 |
L2 and Hilbert Spaces | 189 |
Conditional Expectation | 197 |
Martingales 211 | 210 |
Integration with Respect to a Probability Measure | 51 |
Independent Random Variables | 65 |
Probability Distributions on R 77 | 76 |
Probability Distributions on Rn | 87 |
Characteristic Functions 103 | 102 |
Properties of Characteristic Functions | 111 |
Sums of Independent Random Variables | 117 |
Gaussian Random Variables The Normal and the Multivariate Normal Distributions 125 | 124 |
Supermartingales and Submartingales | 219 |
Martingale Inequalities | 223 |
Martingale Convergence Theorems 229 | 228 |
The RadonNikodym Theorem | 243 |
| 248 | |
| 251 | |
Altre edizioni - Visualizza tutto
Parole e frasi comuni
apply assume balls Binomial Borel bounded calculate called Cauchy Central Limit Chapter characteristic function closed conclude consider constant contains continuous Convergence Theorem Corollary countable deduce defined Definition denote density distribution function equal equivalent example Exercise exists exponential fact Find finite fixed follows function F further G-algebra Gamma Gaussian given gives hence holds hypothesis implies important increasing independent inequality integrable known Lebesgue Let X lim sup Limit Theorem limn linear martingale matrix mean Monotone Moreover nonnegative normal Note observe obtain P(An parameters Poisson positive probability measure Proof prove random variables Recall respect result satisfies sequence Show simple space stopping subset Suppose surely tends theory true uniform unique values variance vector write