Wahrscheinlichkeitstheorie 2

                    -     Stochastic Processes 1

WS 2012 / 2013

(LV-Nr. 3236 L 240 / 241)



office hour
lecturer Prof. Dr. W. König MA 770  by appointment
 koenig "at" wias-berlin.de (030) 203 72547 (WIAS)
(030) 314 29383 (TU B)
M. Wilke Berenguer
MA 784
wilkeber "at" math.tu-berlin.de
(030) 314 25167
M. Salvi
S. Riedel

salvi "at" math.tu-berlin.de
riedel "at" math.tu-berlin.de

Maite offers special office hours for the exams: (please check dates regularly as they might need to be modified)

Friday, February 15th
Monday, March 4th
Friday, March 15th
Tuesday, March 19th

classes (c.t.)

 8h - 10h  
 8h - 10h
 MA 043  
 MA 043
start: 15.10.2012

 MA 649
 MA 649
 MA 376
start: 17.10.2012

start: 25.10.2012

The lectures are taught in English.

The content of all three tutorials will be identical, therefore it is only necessary to attend one of them. Most likely, the first will be in English and the second in German. The language of the third will be determined in class.
You are free to choose your tutorial and there is no need to sign up for it.


A new problem-sheet will be found here every week.
The homework is to be handed in in fixed groups of two to three - preferably three - students before or after the tutorials on Wednesday. To be admitted to the exam you will have to obtain at least 50% of the total possible score in each half of the semester.

 1st Assignment
 2nd Assignment
  3rd Assignment
 4th Assignment   5th Assignment
 6th Assignment
 7th Assignment
 1st half: 1 - 7
 8th Assignment
 9th Assignment
 10th Assignment
 11th Assignment
 12th Assignment
 13th Assignment
 14th Assignment
 2nd half: 8 - 14

Extra points can be obtained by doing the 15th Assignment.


The exam will be in oral form.

Below you can find the doodles for the exams in February and March.

February: http://doodle.com/rdq3p5mkiyx3uvqn

March: http://www.doodle.com/2vam76wtrwb5kwqp Remember to frop the yello form at Ms Willmers' office (MA 774) on the Wednesday preceeding the week of your examination.(Non-TU and BMS students, please contact Maite instead.)

All slots are now filled. If you still need an examination date in March, please contact Prof. König by February 15th!
There will be more offers of dates for oral examinations for the last week of April via Doodle (but not earlier in April). All future examinations from May on will be planned by individual communication.

The examination will be done in English or in German, according to the examinee's wish.

Prof. König has summarised some advice and recomendations for the oral exams for you:

The orals in Probability 2 are based on the lecture notes used and comprise all the material of the lecture and the exercises, but not the parts that were skipped.
The parts that were skipped are the following:
Bsp. 8.2.24
moment problems (Kor. 8.3.5 until Bsp. 8.3.9)
Satz 8.3.22 until the end of Chap. 8
proof of Satz 10.1.14, until excluding Bsp. 10.1.16
notion of mixing, i.e., Def. 10.2.9 until Lemma 10.2.11
Section 11.1
Unlike in homeworks or in written exams, the main weight will be put in the orals on understanding and explaining the matter and the connections and relation between them. Short proofs or surveys of lengthy proofs may be required as well.
Your oral explanations should meet high precision standards and must be well understandable. (If not, the examinator must inquire, and then the examinee's nerves usually start jittering.) In particular, you must make a clear distinction between objects like probability measures, random variables, distribution functions and probabilities, to give an example. Furthermore, the examinator would like to hear full sentences, where appropriate. (Example: On the question "What is the Poisson distribution?", one should not restrict to writing down a formula, but one should also say something like "This is the distribution on the non-negative integers that has these constituent probabilities here.")
 If you formulate a somewhat technical assertion (e.g., a mathematical formula), then you write it down on paper.
Questions may be formulated by the examinator in a somewhat diffuse way by purpose. Then you have the opportunity to direct the exam into the direction of your choice; several good answers may be possible.


The lecture is based on the lecture notes "Wahrscheinlichkeitstheorie 1&2" by Prof. König (Chapters 6-8 and 10-11).
 (Note that this is the new version from July 19th 2012. However, the corrections concern mainly the part corresponding to the lecture "Wahrscheinlichkeitstheorie 1" and the format.)
For the topic of Martingales you can refer to the first chapter of  lecture notes "Stochastische Prozesse II". (This will be topic will be inserted between Chapter 7 and Chapter 8 of the lecture notes "Wahrscheinlichkeitstheorie 1&2".)
The lecture notes are available exclusively in German.