WS 2012/2013, Universität Bielefeld
Probability Theory 240111
This lecture course starts on 17.09.2012 (Monday).
17.09.2012 - 07.10.2012
08.10.2012 - 21.12.2012
- 17.09.2012 (Monday) 16:15-17:45 in V2-200
- 18.09.2012 (Tuesday) 16:15-17:45 in V2-200
- 20.09.2012 (Thursday) 15:30-17:50 in V2-200
- 24.09.2012 (Monday) 15:30-17:50 in U5-133
- 25.09.2012 (Tuesday) 15:30-17:50 in U5-133
- 27.09.2012 (Thursday) 16:15-17:45 in U5-133
- 01.10.2012 (Monday) 16:15-17:45 in V2-200
- 02.10.2012 (Tuesday) 16:15-17:45 in V2-200
- 04.10.2012 (Thursday) 15:30-17:50 in U5-133
- Mondays 16:15-17:45 in T2-204
- Tuesdays 16:15-17:45 in T2-204
- 02.11.2012 (Friday) 12:15-13:45 in T2-241 (Lecture instead of tutorial)
- 09.11.2012 (Friday) 12:00-13:50 in V2-216 (Midterm Exam instead of tutorial)
- 07.12.2012 (Friday) 12:15-13:45 in V2-216 (Lecture instead of tutorial)
Jacod, J. and Protter, P., Probability Essentials, 2nd edition (corrected 2nd printing), Springer, 2004. [Chapters 1-21]
Other useful references:
Rudin, W., Real and Complex Analysis, 3rd edition, McGraw-Hill, 1987. [Chapters 1, 3 and 8]
Dudley, R. M., Real Analysis and Probability, Cambridge University Press, 2002. [Chapters 3, 4, 8 and 9]
- Midterm Exam: 09.11.2012 (Friday) 12:00-13:50 (Sharp) in V2-216
A copy of this version of the lecture note was distributed at the midterm exam.
- Lecture note: Chapters 0, 1 and 2 (Sections 2.5 and 2.7 excluded)
- Problem sets: all Problems and all Exercises up to Problem set 8
- Final Exam: 18.12.2012 (Tuesday) 16:00-17:50 (Sharp) in T2-204
A copy of this version (updated on 07.12.2012) of the lecture note was distributed at the final exam.
- Lecture note: Section 2.7 and Chapters 3 and 4, with the following contents excluded:
Lemma 3.62, Section 3.6, Theorem 4.36, Lemma 4.37, Definition 4.40, Theorem 4.41, Proposition 4.42 and Theorem 4.43.
- Problem sets: all Problems and all Exercises from Problem set 9 to Problem set 14
- (The exam coverage of Midterm Exam is treated as prerequisites.)
Tutorials (Tutor: Holger Sambale, office V5-122, mailbox 223 in V3-128)
17.09.2012 - 21.12.2012
- Fridays 12:15-13:45 in V2-216 (There is no tutorial on 21.12.2012.)
- 05.11.2012 (Monday) 16:15-17:45 in T2-204 (Tutorial instead of lecture)
- 06.11.2012 (Tuesday) 16:15-17:45 in T2-204 (Tutorial instead of lecture)
- 10.12.2012 (Monday) 16:15-17:45 in T2-204 (Tutorial instead of lecture)
- 11.12.2012 (Tuesday) 16:15-17:45 in T2-204 (Tutorial instead of lecture)
Please refer explicitly to this lecture note when quoting any part of it.
Each student is supposed to submit his/her solutions to the following sets of problems.
The deadlines are specified at the beginning of each problem set.
There are two types of problems:
Problems and Exercises.
In each submission of solutions, all Problems are required to be answered
unless otherwise stated, whereas Exercises are only additional and solutions to them are
IMPORTANT: In order to be admitted to the final exam,
each student has to obtain in total more than A/2 points by
submitting his/her solutions to the problem sets,
where A denotes the sum of points assigned to mandatory problems.
Remark: for submission of solutions to the problem sets,
discussion with other students is allowed, but
DO NOT COPY the solutions of others.
Please write your solutions BY YOURSELF, IN YOUR WORDS.
Also it is NOT allowed to submit solutions as a joint work of
two or more students. EACH student is supposed
to submit his/her solutions written in his/her own words.
Points for problem sets:
10 points are assigned to each section of Problems and 15 points to each section of Exercises
unless otherwise stated.
- Problem set 1 (Submission of solutions not required; meant only for discussion in the tutorials.)
- Problem set 2
- Problem set 3 (Some wrong dates have been fixed.)
- Problem set 4 (Some wrong dates have been fixed.)
- Problem set 5
- Problem set 6
- Problem set 7
(The deadline is 12:00 (sharp) on 02.11.2012 (Friday)
since the corresponding tutorial is on 05.11.2012 (Monday).)
- Problem set 8 (Submission of solutions not required; meant only for discussion in the tutorial.)
- Problem set 9
- Problem set 10
DO NOT SKIP Exercise 3.11 when writing your solutions. Exercise 3.11 is not difficult and
will be treated in detail in the tutorial although it is classified as Exercise in regards to the assigned points.
- Problem set 11
- Problem set 12
This time most problems are just simple applications of Theorem 3.61 and Theorem 4.4.
Please try to understand these two theorems.
- Problem set 13
(The deadline is 16:15 (sharp) on 11.12.2012 (Tuesday)
since the corresponding tutorial is on this same day.)
REMARK: Please DO NOT SKIP the Exercises when writing solutions to Problem set 13.
The Exercises in this problem set are not difficult and will be treated in detail in the tutorial although they are classified as Exercises.
- Problem set 14 (Submission of solutions not required; meant only for discussion in the tutorial.)
Department of Mathematics,
Graduate School of Science,
Rokkodai-cho 1-1, Nada-ku, 657-8501 Kobe, Japan
Office: Faculty of Science Building B, Room B426
E-mail: nkajino ``at" math.kobe-u.ac.jp