Probability Theory Autumn 2020
- Prof. Dr. Alain-Sol Sznitman
- Daniel Contreras Salinas
- Time and location
- Tuesday 10:15 - 12:00 and Thursday 10:15 - 12:00 via live streaming. Videos of each lecture will be available shortly after here
This course presents the basics of probability 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 is available for registered students.
Exercise classes will take place every week starting from the 22 of September.
All students will be by default enrolled in the online exercise class. The exercise classes until the end of the semester will take place via Zoom. You will receive the information to access by email. Each Tuesday a recording of one of the exercise classes will be available here.
The exercise sheets will be published on Monday in the table below. The exercises will be
then discussed during the exercise class, and turned in a week later.
Please hand in your solutions by the following Tuesday at 12:00, following the instructions below.
Instructions for submission:
To submit your solutions please follow the steps below:
- Write down your name in the first page of your solutions.
- If you have written your solutions on paper, please scan all the pages in order and create a pdf file. If you do not have a scanner we recommend
that you use applications like CamScanner or OfficeLens. If you wrote your solutions on a tablet, export the file to pdf format.
- Rename your file using your email account followed by the number of the exercise sheet. For example, if your email address is "email@example.com"
and you want to submit the third exercise sheet, you need to rename your file "firstname.lastname@example.org_3.pdf". You can use any mail you prefer here.
- Click on the link corresponding to the exercise sheet and your last name initial letter, enter the password of the lecture and drop your file. You will receive your solutions back to the email
you chose before the next exercise class.
- Files that are not in the format above might not be turned back.
Self evaluation Quiz
You can find your corrected solutions here. The password for your file is the second part of the filename you chose. You can also find the solution of the Quiz here.
- Office hours are offered by group 3 and will take place on Monday and Thursday from 12.00 to 13.00 with a slot reservation system. More information here.
- Each week we will offer 12 slots of 10 minutes via Zoom to answer any question about the lecture or the exercises. We will send you a link to register every Monday at 12:00.
|Tu 15:30-16:30||Calypso Herrera|
|We 11:00-12:00||Daniel Contreras|
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 "Präsenzexemplare" in the mathematics library (HG G 7).