## Probability: A Graduate CourseLike 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. |

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### Contents

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 | |