nature of the course, lecture notes, journal, midterm test, endterm test, time table 2005
This is the homepage of the STATS-course in 2006 of the VGSF-program. The page serves as a basis of communication between students and lecturer. It is updated regularly.
Last update: 13.3.2006
Look up the journal for latest news !
The course is a classroom lecture which is supported by lecture notes.
The lecture notes are not intended to be a self-contained text to be used for self study. The notes are rather an outline of the main concepts and facts. Sometimes the notes contain supplements and facts for which there is no time for presentation during the lecture.
The classroom lecture presents a subset of the notes but sometimes provides more informal explanation and motivation. Diagrams will be drawn on the blackboard and are not copied to the notes. Many facts are formulated in the notes as exercises with or without hints. Some of the exercises will be solved during the lecture, some are home exercises or classroom exercises to be presented by students.
In parts the style of the notes is very formal. Together with informal explanations during the lecture the text should train the students for studying more advanced literature. In order to meet the different skills of the audience (applied, theoretic, formal or informal) the exercises are classified with respect to difficulty and required mathematical skills.
The written exams will be open book exams, meaning that the lecture notes without any additional comments may be used during the exam. The problems of the exams will be exercises of the notes or additional exercises posed in the classroom. The solutions should include extensive references to the notions contained in the notes.
The final collection of those problems where the exams are sampled from will be fixed during the lecture.
The lecture notes are not yet finished. There are some chapters and sections missing (''under construction''). Filling the gaps will be done in the light of student reactions and feedback during the classes. All parts which turn out to be of minor explanatory quality will be improved as far as time allows. Therefore reference numbers of the notes will change from version to version.
I suppose you would like to download the most recent version of the lecture notes.
13.3.2006: Download (final version for the endterm test, no relevant changes)
26.2.2006: Download (more or less final version, up to corrections of errors, no more stuff will be added)
22.2.2006: Download (sections 10.2, 10.3, 11.1 and 11.2 have been reorganized)
5.2.2006: Download (organizational sections have been removed and transferred to the webpage, in line 1 of section 8.4 ''right continuous'' is replaced by ''continuous'')
1.2.2006: Download (improvement of section with conditional expectations, review questions)
31.1.2006: Download (some improvements concerning stochastic sequences, more easy problems, an explanatory discussion of finding expectations of first passage times of random walks)
25.1.2006: Download
The notes on the midterm test are now finished. These notes contain full lists of problems and questions, and the evaluation scheme. Moreover, the solution file for the problems of the midterm test has started.
Texfiles: Download
For extraordinary discussions of review questions there are up to 3 points available. Every correct solution of an easy problem gives 1 point, of an intermediate problem gives 2 points and of an advanced problem gives 3 points.
If for a problem number more than one version (easy, intermediate or advanced) is solved then the version with the best solution counts for evaluation.
IMPORTANT: Since there are only 9 advanced problems presently, we have to avoid that only the solutions of these problems are learned by heart. Therefore only up to at most three advanced problems count for the evaluation. It should be noted that the solutions of advanced problems will be checked and evaluated with rigor. Therefore it might be reasonable to provide the solutions of the corresponding easy or intermediate problems, too.
The endterm test will contain 10 problems A, 5 problems B and 1 problem C.
Evaluation scheme:
For the Midterm test points 20, 22, 24 or 26 are counted, depending on the marks 1, 1*, 1** or 1***. For the endterm test each problem A counts 2 points, each problem B counts 3 points and problem C counts 5 points. The final points are obtained as an average of the points of the midterm test and the endterm test, rounded up to the next integer.
Grades are given as follows: 1 for >= 20, 2 for 17-19, 3 for 14-16, 4 for 11-13.
For passing the exam at least 11 points have to be achieved on the endterm test.
For internal ranking special honors are given: 1* for 22-23, 1** for 24-25, 1*** for >= 26.
Last version of the lecture notes.
Final version of the problem collection for the endterm test.
Evaluation scheme for the endterm test and the course.
Solution of problem 13-30 for dowload.
The full version of the notes is ready for download. They will only be changed due to errors and misprints.
A new version of the problem list for the endterm test is ready. The problem lists are now complete. The review questions a still under construction.
22.2.2006
A new version of the notes is available. Note that the notes will be now updated frequently. Therefore print only those parts which are new !
The notes on the endterm test have been started. Up to now there is no evaluation scheme. In contrast to the midterm test there will be no exchangeability between problems of type A, B and C.
The grading scheme of the midterm test has been cancelled. The midterm test will have influence on the final mark only through the points achieved. Final mark 1 will be based on a minimal point limit in the midterm test and in the endterm test.
9.2.2006
The second latex file with student solutions came on 9.2. in the afternoon and has been returned with corrections on 9.2. in the evening.
The scale scale of marks for the midterm test has been changed according to the suggestions of the students group.
Some misprints in the list of questions and problems for the midterm test have been corrected.
The first latex file with student solutions came on 7.2. in the evening and has been returned with corrections on 8.2. in the evening.
Unit 16 will not be an exercise lesson. We will start with the financial market picture.
Future exercise lessons will not be organized as student's presentations. They rather will be devoted to repetitions and helpful hints for the solutions of problems for the endterm test. The students are expected to start with the written preparation of the problem solutions from the very beginning of the second part. Therefore there will be a list of problems for endterm test which is supplemented regularly. In this separate list the numbering will be kept fixed.
Midterm test: Advanced problems 10 and 11 have been deleted. The reason is that they are covered by Theorem 8.57. Now there are only 9 advanced problems. Therefore we have do avoid abuse of the small number of advanced problems. This is done by a minor modification of the evaluation scheme. See Midterm test.
The file with problem solutions for the Midterm test has been started. At the moment there are only the solutions of the problems related to the Wiener process, prepared by the lecturer. Further solutions are added as soon as they are provided by the students group. See Midterm test.
We agreed that problem numbers are useless for referencing since numbers are changing every day. Instead the texfile of the problem lists (see Midterm test) may be used by the student class to provide solutions with full quotation of problem statements.
The student class together with staff members will make suggestions of recoding the evaluation scheme into American grades.
30.1.2006
We have to shift the last lecture. Instead of 9.3.2006 there will be a lecture on 20.2.2006.
30.1.2006
We fixed date and time of the tests.
Midterm test: Monday,13.2.2006, 18:00, Seminar room of the Department of Statistics, WU.
Endterm test: Thursday, 23.3.2006, 18:00, Seminar room of the Department of Statistics, WU.
Where it is: Go by U4 to Spittelau. Leave the station and go to the white building that looks like a tower. This is the UZA2, center for statistics and computer science. The seminar room is located on the 4th floor on the left hand side .
How much time do you have: I think we should allocate 120 minutes.
You may use the latest version of the lecture notes. The test will consist of 3 review questions and 7 problems. A full list of review questions will be provided by the end of this week. Problems are part of those we have posed as exercises. More details are provided shortly.
The following time table contains the preliminary schedule of the course from january to march 2006.
| Calendar week | Unit | Subjects |
| 2 | 1 | measure and probability |
| 2 | measure and probability | |
| 3 | measurable functions and random variables | |
| 3 | 4 | exercises |
| 5 | integrals and expectation | |
| 6 | integrals and expectation | |
| 7 | integrals and expectation | |
| 4 | 8 | exercises |
| 9 | conditional expectation | |
| 10 | stochastic sequences (gambling) | |
| 11 | stochastic sequences (martingales) | |
| 5 | 12 | exercises |
| 13 | Wiener process | |
| 14 | Wiener process (first passage times) | |
| 15 | Wiener process (stopping times) | |
| 6 | Skiing | |
| 7 | 16 | exercises |
| 17 | the financial market picture (discrete time trading) | |
| 18 | stochastic calculus (Stieltjes integral, differential notation) | |
| 19 | stochastic calculus (semimartingales, stochastic integrals) | |
| 8 | 20 | exercises |
| 21 | stochastic calculus (Ito calculus) | |
| 22 | applications (Black Scholes model) | |
| 23 | exercises | |
| 9 | 24 | linear stochastic differential equations |
| 25 | martingales and stochastic integrals | |
| 26 | martingales (Levy's characterization, martingale representation) | |
| 10 | 27 | martingales (Girsanov theorem) |
| 28 | exercises |