# Stochastic Processes WS 17/18

## News

[16.02.18] There is news about the retake exam. Check the exam section![02.02.18] We changed exercise H1 a) and H2 of sheet 14 slightly.

[08.01.18] There is news about the exam. Check the exam section!

[21.12.17] Here is a note on H2 of sheet 5. In the exercise class it was assumed that the process on sheet 2 converged to Brownian bridge in distribution, however on we only proved this for the finite dimensional distributions. This note now gives the proof assuming only the convergence of the finite diminensional distributions.

[01.12.17] In the week of 11-17 December the exercise class and the Thursday lecture will be swapped.

[01.12.17] We changed exercise H4 of sheet 7 to be somewhat easier and added a hint.

[09.11.17] There will be no lecture on Thursday, the 16th of November.

[09.11.17] Exercise H2 of sheet 4 has been formulated more precisely.

[09.10.17] There will be a lecture instead of an exercise class on Tuesday in the first week. (17th of October)

## Times and locations

Lecture: | Monday 14:10-15:50 | B004 | Christian Hirsch |

Thursday 14:15-16:00 | B004 | ||

Exercise Class: | Tuesday 14:15-16:00 | B004 | Thomas Beekenkamp |

## Registration

Please register for the course here.## Exercises and Homework

**Sheets:**

Due on | Solutions | |

Sheet 1 | Tuesday, October 24th | Solutions |

Sheet 2 | Monday, October 30th | Solutions |

Sheet 3 | Tuesday, November 7th | Solutions |

Sheet 4 | Tuesday, November 14th | Solutions |

Sheet 5 | Tuesday, November 21st | Solutions |

Sheet 6 | Tuesday, November 28th | Solutions |

Sheet 7 | Tuesday, December 5th | Solutions |

Sheet 8 | Thursday, December 14th | Solutions |

Sheet 9 | Tuesday, December 19th | Solutions |

Sheet 10 | Tuesday, January 9th | Solutions |

Sheet 11 | Tuesday, January 16th | Solutions |

Sheet 12 | Tuesday, January 23rd | Solutions |

Sheet 13 | Tuesday, January 30th | |

Sheet 14 | Tuesday, February 6th |

The exercise sheets are posted every Tuesday, the homework will be due on the next Tuesday at 14:00. Please put your homework in homework box 56 on the first floor, or hand it in during the exercise class.

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.

## Course Outline

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

## 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 - G. Last and M. Penrose,
*Lectures on the Poisson Process*, 2017. Link

- Lecture notes on Poisson processes and point processes - R. Durrett,
*Probability. Theory and Examples*, 4th edition, Cambridge University Press 2010. Link

- Contains all the basics in probability theory

## Exam

The oral exam took place on the 14th, 15th and 16th of February.The retake exam took place on the 12th and 13th of March.