An Introduction to Measure Theoretic Probability

Lecturer:

Class Teacher:

Imma Curato

  Antonia Mayerhofer

block course 05.10 - 9.10

05.10.2015: Lecture: 8:45-12:00 He18, 2.20.

06.10.2015: Lecture: 8:45-10:15  He18, 2.20;   Tutorial: 10:30-12:00  He18, 2.20.

07.10.2015: Lecture: 9:30-12:00 He18, 2.20. 

08.10.2015: Lecture: 9:30-12:00 He18, 2.20. 

09.10.2015: Exercises: 8:45-10:15 He18, 2.20;  Exercises: 10:30-12:00  He18, 2.20 .

22.10.2015: Tutorial: 14:15-15:00 He22, E18; 23.10.2015: Exercises: 12:15-13:45 He18, 2.20

from the 12.10  until Christmas

Lecture: Monday 10-12 He18, 2.20

Exercises: Wednesday 10-12  He22, Room 202

Tutorial: Wednesday 18:00 - 18:45 He18 E20 (to 02.12.15)

LAST Exercise Class: Wednesday, 09.12. 18:00 - 19:30 He18 E20

Tutorial: Thursday, 07.01.16 10-12 in H9

Final exam:

written exam: 15/01/2016 H11, 15:15-16:45

Details:  An Introduction to Measure Theoretic Probability is an open exam.

Authorized Auxiliaries:

• a non-programmable calculator (no smartphone),
• one A4 sheet or equivalent 2 pages of handwritten notes,
• a permanent pen.

The results are now available in the Hochschulportal.

Post exam review: 20.01.2016, 10-12, HeHo 18 Room 2.03.

The second written exam will take place  07/04/2016 He220, 10:30-12:00
 

To register for the second written exam, please write an email to Imma Curato with your name, immatriculation number and course of study.

The registrations are open until the 6th April due to technical problems with the HSP.

Lecture Notes:

Exercise Sheets:

Lecture notes (06.12.2015)

Exercise Sheet 1

Exercise Sheet 2

Exercise Sheet 3

Exercise Sheet 4

Exercise Sheet 5

Exercise Sheet 6

Exercise Sheet 7

Exercise Sheet 8

Exercise Sheet 9

Solution (Sheet 4 Ex 23 2.)

This course covers the basic facts from probability in a measure-theoretic approach.

Specific topics are

• definition and properties of measure and Lebesgue integral
• the fundamentals of probability: probability space, random variables, conditional expectation, modes of convergence, convolutions and characteristic functions, central limit theorem
• the fundamentals of statistics: simple random sampling, introduction to estimation techniques

Literature:

• H. Bauer, Measure and Integration Theory, De Gruyter Studies in Mathematics, 2011
• H. Bauer, H., Probability Theory, De Gruyter Studies in Mathematics, 2011
• P. Billingsley, Probability and Measure, Wiley Series in Probability and Statistics
• W. Rudin. Real and Complex Analysis, McGraw-Hill International Editions, 1987
• J. Jacod & P. Protter, Probability Essentials, 2nd edition, Springer, 2004.
• E. Kopp, J. Malczak & T. Zastawniak, Probability for Finance, Cambridge University Press, 2014
• R. Leadbetter, S. Cambanis, V. Pipiras, A Basic Course in Measure and Probability, Cambridge University Press, 2014
• A. N. Shiryaev, Probability, 2nd edition, Springer, 1995.
• D. Williams, Probability with Martingales, Cambridge University Press, 1991.

Refresher in Probability 1

Refresher in Probability 2