## Probability Theory: A Comprehensive CourseThis second edition of the popular textbook contains a comprehensive course in modern probability theory, covering a wide variety of topics which are not usually found in introductory textbooks, including: The theory is developed rigorously and in a self-contained way, with the chapters on measure theory interlaced with the probabilistic chapters in order to display the power of the abstract concepts in probability theory. This second edition has been carefully extended and includes many new features. It contains updated figures (over 50), computer simulations and some difficult proofs have been made more accessible. A wealth of examples and more than 270 exercises as well as biographic details of key mathematicians support and enliven the presentation. It will be of use to students and researchers in mathematics and statistics in physics, computer science, economics and biology. |

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#### LibraryThing Review

User Review - cpg - LibraryThingAmazingly well-done I taught a course in advanced probability out of the first half of Klenke's _Probability Theory_ during Fall 2009 at Brigham Young University, and I'm just starting to teach the ... Read full review

### Contents

1 | |

Independence | 47 |

Generating Functions | 77 |

The Integral | 85 |

Moments and Laws of Large Numbers | 101 |

Convergence Theorems | 131 |

LpSpaces and the RadonNikodym Theorem | 145 |

Conditional Expectations | 169 |

Markov Chains | 351 |

Convergence of Markov Chains | 389 |

Markov Chains and Electrical Networks | 411 |

Ergodic Theory | 439 |

Brownian Motion | 457 |

Law of the Iterated Logarithm | 509 |

Large Deviations | 521 |

The Poisson Point Process | 543 |

Martingales | 189 |

Optional Sampling Theorems | 205 |

Martingale Convergence Theorems and Their Applications | 217 |

Backwards Martingales and Exchangeability | 231 |

Convergence of Measures | 245 |

Probability Measures on Product Spaces | 273 |

Characteristic Functions and the Central Limit Theorem | 294 |

Inﬁnitely Divisible Distributions | 331 |

The Itô Integral | 563 |

Stochastic Differential Equations | 589 |

Notation Index | 613 |

References | 617 |

625 | |

628 | |