Please email H. Bruin for further information about this course.

Day | Time | Lecture room | from | until | |
---|---|---|---|---|---|

Tuesday | 11:30-13:00 | SR07 | Lecture | 2.10.2018 | 29.01.2019 |

Thursday | 8:30-9:15- | SR10 | Exercises | 4.10.2018 | 24.01.2019 |

Thursday | 9:30-10.15 | SR10 | Lecture | 4.10.2018 | 24.01.2019 |

- Script Jiří Černý (in German)
- Script Franz Hofbauer (in German)
- Script Markov chains script (in English)
- Script Josef Hofbauer (in English).
**This script was written by students in Hofbauer's class and hasn't been proof-read in full!** - P. Billingsley, Probability and Measure 3rd Edition ISBN-13: 978-0471007104 ISBN-10: 0471007102
- Kai Lai Chung, Elementary probability and stochastic processes, Springer Verlag New York, 1974. ISBN 0-387-90159-0
- E. Çinlar, Introduction to Stochastic Processes, Dover Publications Inc. 2013 ISBN-13: 978-0486497976 ISBN-10: 0486497976
- W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition 3rd Edition. ISBN-13: 978-0471257097 ISBN-10: 0471257095
- G. R. Grimmet and D. R. Stirzaker, Probability and Random Processes, Oxford Science Publications 1981, Clarendon Press Oxford ISBN 0-19-853185-0
- C. Norris, Markov Chains, (Cambridge Series in Statistical and Probabilistic Mathematics) Cambridge Univ. Press, ISBN-13: 978-0521633963 ISBN-10: 0521633966
- G. Grimmett, D. Welsh, Probability: An Introduction, Oxford Science Publ. ISBN 0 19 853264

**Written** Exam for the VO, class tests + presenting exercises on the board
for Proseminar (Exercises).

Day | Material | |
---|---|---|

Week 1 | ||

2/10/2018 | Introduction, Poisson Limit Theorem, CLT | |

4/10/2018 | Poisson Limit Theorem, CLT | |

Week 2 | ||

9/10/2018 | Random walks on graphs, Gambler's Ruin | Norris, Chapter 1 |

11/10/2018 | Exercise sheet 1-4 | |

Week 3 | ||

16/10/2018 | Gambler's Ruin/Absorbing states | |

18/10/2018 | Finite Markov chains/communication classes Stationary distributions | Norris, Chapter 1 |

Week 4 | ||

23/10/2018 | Henna Koivusalo will replace me this week Stopping times | Grimmett & Stirzaker Sect 7.7 and 7.9 |

25/10/2018 | Exercise sheet 6-11 | |

Week 5 | ||

30/10/2018 | Time-reversible Markov chains | Norris, Section 1.9 |

1/11/2018 | No class because of All Souls | |

Week 6 | ||

6/11/2018 | Random walks on Z | Script J. Hofbauer, Section 1.1-1.5 |

8/11/2018 | Exercise sheet 11-15 | |

Week 7 | ||

13/11/2018 | Random walks, Reflection Principle Ballot Theorem | Script J. Hofbauer, Section 1.1-1.5 |

15/11/2018 | Cancelled | |

Week 8 | ||

20/11/2018 | Arcsine Laws, Random walks and Brownian motion Counting processes | Script J. Hofbauer, Section 1.6 |

22/11/2018 | Exercise sheet 15-19 | |

Week 9 | ||

27/11/2018 | Characterisations Poisson Process | Script Černý, Kapitel 3 |

29/11/2018 | more on Poisson processes | Script Černý, Kapitel 3 |

Week 10 | ||

4/12/2018 | Lecture by Martin Huesmann Differential equation for generating function | Grimmett and Stirzaker Section 6.8 |

6/12/2018 | Class Test (material exercises 1-14 and variations) | |

Week 11 | ||

11/12/2018 | Class canceled | |

13/12/2018 | Class canceled | |

Week 12 | ||

8/1/2019 | Birth and Death processes Differential equation for generating function | Grimmett and Stirzaker 6.11 |

10/1/2019 | Exercise sheet 18-22 | |

Week 13 | ||

15/1/2019 | Backward/Forward equations and solutions | Grimmett and Stirzaker 6.8 |

17/1/2019 | Exercise sheet 21,22,23,24,26 | |

Week 14 | ||

22/1/2019 | 15:00-16:30 in SR9 | |

24/1/2019 | Class Test (material exercises 15-20 and variations) | |

Week 15 | ||

29/1/2019 | Written Exam 15:00-17:00 HS5 | |

31/1/2019 |

Updated August 16 2019