Probability: A Graduate CourseSpringer Science & Business Media, 17 oct. 2012 - 602 pages Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references. |
Table des matières
1 | |
A GraduateCourse 2 Random Variables | 25 |
A GraduateCourse 3 Inequalities | 118 |
A GraduateCourse 4 Characteristic Functions | 157 |
A GraduateCourse 5 Convergence | 201 |
A GraduateCourse 6 The Law of Large Numbers | 264 |
A GraduateCourse 7 The Central Limit Theorem | 329 |
A GraduateCourse 8 The Law of the Iterated Logarithm | 383 |
A GraduateCourse 9 Limit Theorems Extensions and Generalizations | 423 |
A GraduateCourse 10 Martingales | 467 |
A GraduateCourse AppendixSome Useful Mathematics | 555 |
577 | |
587 | |