# Stochastic Processes WS 18/19

## News

[17.10.2018]: The first exercise session will take place on 23.10.2018. The first exercise sheet will be released after the first exercise session, its solutions will be presented in the second exercise session (30.10.2018).

[25.10.2018]: There will be no lecture on Thursday, 29.11.2018; instead, a lecture will take place on Wednesday, 31.10.2018, from 10 to 12 in room A027!

[31.10.2018]: Here you can find the script of the lecture from 31.10.2018, where Brownian motion was introduced (including a proof of existence).

[08.11.2018]: Here you can find a short overview on Markov processes, which was handed out in today's lecture.

[18.12.2018]: Exercise sheet 8 was replaced by a corrected version (Exercise 1(a) and the upper bound in the claim of Exercise 4 were corrected).

[07.01.2019]: As announced in today's lecture, the exercise session on Tuesday, 08.01.2019, and the lecture on Thursday, 10.01.2019, will be switched - a lecture will take place on Tuesday (14-16) and the exercise session will take place on Thursday (14-16).

[08.01.2019]: Here you can find the script of the lecture from 08.01.2019.

[21.01.2019]: The link for the registration to the oral exam is now online. You can find it below in the exam section.

[22.01.2019]: Here you can find the script of the next lecture (Thursday, 24.01.2019).

[08.02.2019]: Here you can find the updated version of the script including the last lecture of the course.

[11.02.2019]: The schedule for the the oral exam is now online. You can find it below in the exam section.

[05.03.2019]: The link for the registration to the retake exam is now online. You can find it below in the exam section.

## Times and locations

 Lecture: Monday 14-16 B004 Sabine Jansen Thursday 14-16 B004 Exercise Class: Tuesday 14-16 B004 Leonid Kolesnikov
Please check the news section for cancellations and room changes.

## Exercises and Homework

Sheets:
 Due on Solutions Sheet 1 30.10.2018 - Sheet 2 06.11.2018 - Sheet 3 13.11.2018 - Sheet 4 20.11.2018 - Sheet 5 27.11.2018 - Sheet 6 04.12.2018 - Sheet 7 11.12.2018 - Sheet 8 (corrected) 18.12.2018 - Sheet 9 10.01.2019 - Sheet 10 15.01.2019 - Sheet 11 22.01.2019 - Sheet 12 29.01.2019 - Sheet 13 05.02.2019 -

The exercise sheets (homework) will be released weekly. The solutions are to be handed in before the weekly exercise sessions, in which the solutions will be discussed/presented. Additionally, the students will have the opportunity to ask questions concerning the contents of the lecture during the exercise sessions.

Though there will be no bonus points system, we want to encourage the students to do and hand in the exercises.

## Course Outline

The following topics will be treated in the course:
1. Basic Notions
2. Brownian motion
3. Markov chains
4. Feller processes
5. Interacting particle systems

## Literature

The main reference for this course is
• T. M. Liggett, Continuous Time Markov Processes, AMS 2010.
Also, parts of the lecture notes by Prof. Michael Scheutzow will be of relevance, which can be found at StoProII (in English) and StoMod (in German). Further references and background can be found in
• R. Durrett, Probability - Theory and Examples, 4th edition, Cambridge Univ. Press 2010.
• D. Levine, Y. Peres and E.L. Wilmers, Markov Chains and Mixing Times, AMS 2009.
• L. Koralev and Ya. Sinai, Theory of Probability and Random Processes, 2nd edition, Springer 2012.

## Exam

The regular exam will take place in the second week of the semester break. It will be an oral exam. (Registration closed!)
You can register here for the retake exam! It will take place from 17.04 to 19.04.