Probability theory [MA2409]

News

exam: August 8, 2012, 15:00 - 16:30 in MW 2001
post-exam review: August 13, 2012, 11:00 - 12:30 in MI 03.10.011
second exam: September 26, 2012, 8:00 - 09:30 in Interims-Hörsaal 1 (new room!)
post-exam review: October 4, 09:30 -10:30 in MI 03.12.020 (Glaskasten)

Lecturer: Prof. Dr. Silke Rolles
Time and location of the lecture:

Tuesday 8:15 – 9:45 MW 1801

Friday 8:15 – 9:45 MI HS 1
Prerequisites: Maß- und Integrationstheorie (MA 2003) and Einführung in die Wahrscheinlichkeitstheorie (MA 1401)
Literature: The books will be on reserve in the library (Semesterapparat).
- Measure theory:
  - M. Brokate, G. Kersting: Maß und Integral, Birkhäuser, 2010. Link to the ebook
  - The appendix of R. Durrett: Probability: theory and examples, fourth edition, Cambridge University press, 2010.
- Probability theory:
  - P. Billingsley: Probability and measure, third edition, Wiley, 1995.
  - K.L. Chung: A course in probability theory, third edition, Academic Press, 2001.
  - R. Durrett: Probability: theory and examples, fourth edition, Cambridge University press, 2010.
  - A. Klenke: Wahrscheinlichkeitstheorie, 2. Auflage, Springer, 2008. Link to the ebook of the first edition
  - A. Klenke: Probability theory, Springer, 2008.
  - D. Williams: Probability with martingales, Cambridge University Press, 2005.
Syllabus
Lecture notes will be posted in TUM-Online approximately one week after the lecture.

Tuesday	8:15 – 9:45	MW 1801
Friday	8:15 – 9:45	MI HS 1

Homework will be assigned every week. Every Tuesday a problem sheet will be handed out during the lecture. You should try to solve all homework problems. You can work in groups of up to 3 students. Your solutions can be written in German or in English. Please put your solutions in the mailbox "probability theory" in the basement of the mathematics building. Your homework is due on Tuesday at 12:00 one week after it was assigned.
Graded homework will be returned during the tutorials one week after it was handed in. Homework which is not picked up during the tutorials can be found in the shelf located on the right-hand side after the first glass door in building part 03.12.
Grades on homework: Each exercise is graded from 0 to 4 points, where 4 stands for a perfect solution, 3 for few minor mistakes or missing arguments, 2 for major lacks and 1 for reasonably worked on. If an exercise consists of several parts, each of them has to be worked out reasonably for the whole exercise to count as reasonably worked out.
Final grade: The final grade is the grade obtained in the final exam plus a possible bonus. If 80% of all homework problems are reasonably worked out, then you get a bonus: If you pass one of the final exams (i.e. your grade is 4.0 or better), then your grade is improved by 0.3 (for example 4.0 becomes 3.7, 3.7 becomes 3.3, 3.3 becomes 3.0 etc.). A grade of 1.0 is not changed.

Time and location of the tutorials:

Group	time	location	tutor
1	Thursday, 08:00 - 10:00	MI 03.06.011	Thomas Kochler
2	Thursday, 12:00 - 14:00	MI 02.04.011	Thomas kochler
3	Friday, 10:00 - 11:30	MI 02.04.011	Julia Wagner
4	Friday, 10:00 - 12:00	MW 0337 ~~MI 02.08.020~~	Johannes Keller
5	Friday, 10:00 - 12:00	MI 02.10.011	Mathias Rafler
6	Friday, 12:00 - 14:00	MI 03.08.011	Mathias Rafler

Teaching assistants: Johannes Keller, Renate Klaffki, Thomas Kochler, Mathias Rafler, Franz, Rembart, Julia Wagner

Monday, May 21, 16:15 - 17:45, MW 0001: types of convergence of random variables and relations, Borel-Cantelli lemma, tail-sigma-algebra and Kolmogorv's 0-1-law, product spaces and independence
Monday, June 25, 16:15 - 17:45, MW 0001: weak convergence, characteristic functions, Levy's continuity theorem and central limit theorems
Monday, July 16, 16:15 - 17:45, IHS 2: conditional expectation, martingales, martingale convergence theorems, martingale inequalities

Problem sheet	Topic	Due date	Comments
Sheet 1	probability measures and measurability	April 24
Sheet 2	inequalities	May 2
Sheet 3	independence infinte products	May 8
Sheet 4	independence and convergence	May 15	T4.1: X_n independent
Sheet 5	convergence and sums	May 22
Sheet 6	0-1 law, SLLN, weak convergence	May 30	see additions to 6.3
Sheet 7	weak convergence, a central limit theorem	June 5	7.2(b): Asymptotik ist k_n/sqrt{n/2}
Sheet 8	characteristic functions	June 12
Sheet 9	characteristic functions and central limit theorem	June 19	lambda_i is a version of a_i
Sheet 10	conditional expectation	June 26	u in T10.1 added
Sheet 11	conditional expectation, martingales	July 3	11.3(b): Y_n identically distributed
Sheet 12	martingale application	July 10
Sheet 13	martingale application	July 17