An Introduction to Measure Theoretic Probability

News:

There is a block course in the last week before the lecture regularly starts, so from 9th of Oct. until 12th of Oct. 2017

The schedule is as follow:

• Mon., 09.10.2017: Lecture:  08:45-10:15  He18,  1.20.   Tutorial:   10:30-12:00  He18,  1.20.
• Tue.,  10.10.2017:  Lecture:  08:45-10:15  He18,  2.20.   Lecture:   10:30-12:00  He18,  2.20.
• Wed., 11.10.2017:  Lecture:  08:45-10:15  He18,  2.20.   Exercise Class:  10:30-12:00  He18,  2.20. 
• Thu.,  12.10.2017:  Lecture:  08:45-10:15  He18,  2.20.    Lecture:  10:30-12:00  He18,  2.20.   Exercise Class:  13:00-14:30  He18,  2.20.

• Lecture: Monday,  10:00-12:00, He18 2.20
• First  Lecture:  16/10/2017
• Tutorial course: Wednesday, 08:00-09:00, He22 E04
• First  Tutorial course:  18/10/2017
• Exercise class: Wednesday,  09:00-10:00, He22 E04
• First  Exercise class: 18/10/2017
• Extra classes and tutorials: Friday, 08:00-10:00 He22 E03 (27.10., 03.11., 01.12., 08.12., 15.12.)

Final Exam:

Final Exam: written, closed,   90 minutes.

1. 19th of January  2018, 12:15-13:45 in He. 18, 1.20.

2. 08th of March 2018, 10:15-11:45 in He. 18, 1.20.

To participate in the written exam, you have to register at campusonline.uni-ulm.de, until Monday, 15th of January 2018.

Prerequisites:

Analysis I+II and Linear Algebra I.

Contents:

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.
• An introduction to statistics: simple random sampling, introduction to estimation techniques.

 Literature:

• H. Bauer, Measure and Integration Theory, De Gruyter Studies in Mathematics, 2011.
• H. Bauer, Probability Theory, De Gruyter Studies in Mathematics, 2011.
• P. Billingsley, Probability and Measure, Wiley, 2012.
• 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.

Exercise sheets:

Moodle 

Moodle

Refresher in Probability 1

Refresher in Probability 2