# Stochastic Processes WS 16/17

## Registration

Please register for the course here.## News

[01.02.17] The schedule for the exam is out. Check the exam section![25.01.17] There is more information available on the exam. Check the exam section!

[22.12.16] There will be no exercise sheet in the first week of the new year; there should be enough material on Sheet 9 to keep you entertained. The deadline for Sheet 9 has been extended for an extra week.

[20.10.16] The lecture on Thursday, November 3, will take place in B052.

[20.10.16] There will be no exercise class on the 1st of November.

## Times and locations

Lecture: | Monday 10:00-12:00 c.t. | B 0005 | Markus Heydenreich |

Thursday 14:00-16:00 c.t. | B 0005 | ||

Exercise Class: | Tuesday 14:00-16:00 c.t. | B 0004 | Thomas Beekenkamp |

## Exercises and Homework

**Sheets:**

Due on | Solutions to tutorial exercises | |

Sheet 1 | Monday, October 31st | Solutions 1 |

Sheet 2 | Monday, November 7th | Solutions 2 |

Sheet 3 | Monday, November 14th | Solutions 3 |

Sheet 4 | Monday, November 21st | Solutions 4 |

Sheet 5 | Monday, November 28th | Solutions 5 |

Sheet 6 | Monday, December 5th | Solutions 6 |

Sheet 7 | Monday, December 12th | Solutions 7 |

Sheet 8 | Monday, December 19th | Solutions 8 |

Sheet 9 | Monday, January 16th | Solutions 9 |

Sheet 10 | Monday, January 23rd | Solutions 10 |

Sheet 11 | Monday, January 30th | Solutions 11 |

Sheet 12 | Monday, February 6th | Solutions 12 |

The exercise sheets are posted every Monday, the tutorial exercises are for the exercise class on Tuesday and the homework will be due on the next Monday. Please put your homework in homework box 56 on the first floor.

You can get a bonus for your grade, the height of which depends on the amount of points obtained from the homework exercises, with thresholds at 50% and 75% of the total amount of points. To keep track of your points it is

**necessary that you are registered**for the course. The homework is to be handed in individually, but working together is strongly encouraged.

The homework will be graded by Florian Ingerl, he can be reached at imelflorianingerl [AT] gmail [DOT] com. It will be handed back in the exercise class in the next week, any leftover homework will be deposited in the return box.

## Course Outline

The following topics will be treated in the course:- Basic Notions
- Brownian motion
- Markov chains
- Feller processes
- Interacting particle systems

Lecture notes of last year written by a student can be found here.

**Disclaimer:**these notes have not been checked for correctness and the content of this years course may vary.

## Literature

The main book for this course is- T.M. Liggett,
*Continuous Time Markov Processes*, AMS 2010.

- L.B. Koralov and Ya. Sinai,
*Theory of Probability and Random Processes*, 2nd edition, Springer 2010.

- An alternative presentation of the material - A. Klenke,
*Probability Theory*, Springer 2014.

- An even different presentation of the material, also available in German - P. MÃ¶rters, Y. Peres,
*Brownian Motion*, Cambridge University Press 2010. Link

- Specifically for the chapter on Brownian motion - D.A. Levin, Y. Peres, E.L. Wilmer,
*Markov Chains and Mixing Times*, AMS 2009. Link

- Specifically for the chapter on Markov chains - R. Durrett,
*Probability. Theory and Examples*, 4th edition, Cambridge University Press 2010. Link

- Contains all the basics in probability theory