- Lecturer
- Alain-Sol Sznitman
- Coordinator
- Chong Liu
- Time and Location
- Tuesday 10:15 -- 12:00 and Thursday 10:15 -- 12:00 in HG G 3

This course presents the basics of probability theory and the theory of stochastic processes in discrete time. The following topics are planned: Basics in measure theory, random series, law of large numbers, weak convergence, characteristic functions, central limit theorem, conditional expectation, martingales, convergence theorems for martingales, Galton Watson chain, transition probability, Theorem of Ionescu Tulcea, Markov chains.

An electronic version of the lecture notes will be available for registered students.

A printed version will be available for purchase (CHF 15) upon sufficient demand.

The exercise sheets will be published here on Monday as well as distributed on Tuesday during the lecture. The exercises will then be discussed during the exercise class, and turned in a week later.

If you cannot come to the exercise class, you may submit your work by dropping it in your assistant's tray located in HG G53-54 (please do so no later than the beginning of the respective exercise class). Solutions will be available on this page after the deadline for handing in.

exercise sheet | due by | solutions |
---|---|---|

Exercise 1 | Oct. 02 | Solution 1 |

Exercise 2 | Oct. 09 | Solution 2 |

Exercise 3 | Oct. 16 | Solution 3 |

Exercise 4 | Oct. 23 | Solution 4 |

Exercise 5 | Oct. 30 | Solution 5 |

Exercise 6 | Nov. 06 | Solution 6 |

Quiz | Nov. 08 | Quiz solution |

Exercise 7 | Nov. 13 | Solution 7 |

Exercise 8 | Nov. 20 | Solution 8 |

Exercise 9 | Nov. 27 | Solution 9 |

Exercise 10 | Dec. 04 | Solution 10 |

Exercise 11 | Dec. 11 | Solution 11 |

Exercise 12 | Dec. 18 | Solution 12 |

Exercise 13 | Dec. 20 | Solution 13 |

**First exercise class:** Tuesday Sep. 25.

**Office hours ("Praesenz''):** Mondays and Thursdays 12:00 - 13:00 in HG G 32.6

**Time and places:**(provisional)

time | room | assistant | students |
---|---|---|---|

Tu 13-14 | HG F 26.5 | Daniel Balint (daniel.balint@math.ethz.ch) | An-Gu |

Tu 13-14 | ML H 41.1 | Daniel Contreras Salinas (daniel.contreras@math.ethz.ch) | Ha-Lang |

Tu 14-15 | HG F 26.5 | Daniel Balint (daniel.balint@math.ethz.ch) | Lanz-Sa |

Tu 14-15 | ML H 41.1 | Chong Liu(chong.liu@math.ethz.ch) | Sch-Zh |

**Self evaluation quiz** (during the lecture): 10:15 - 11:15, Thursday, November 08.

- R. Durrett, Probability: Theory and examples, Duxbury Press 1996. Chapter 1 and Appendix A of this book contain a summary of measure theory. (Online Version)
- H. Bauer, Wahrscheinlichkeitstheorie, 4. Auflage, de Gruyter Lehrbuch 1991
- J. Jacod and P. Protter, Probability essentials, Springer 2004 (Online Version)
- A. Klenke, Wahrscheinlichkeitstheorie, Springer 2008 (Online Version)
- D. Williams, Probability with martingales, Cambridge University Press 1991 (Online Version)

The online versions are available online via NEBIS.

These books are available as "Praesenzexemplare" in the mathematics library (HG G 7).