An Introduction to Measure Theoretic Probability

Lecturer:

Imma Curato

Class and Tutorial Teacher:

Dirk Brandes

News:

There is a block course in the week before the regular start of the lecture period, so from 8th of Oct. until 12th of Oct.

The schedule is as follow:

• Mon., 08.10.2018: Lecture: 8:45-10:15 He18, 2.20. Lecture: 10:30-12:00 He18, 2.20.
• Tue.,  09.10.2018:  Tutorial: 8:45-10:15 He18, 2.20. Lecture: 10:30-12:00 He18, 2.20.
• Wed., 10.10.2018:  Lecture: 8:45-10:15 He18, 2.20. Exercise Class: 10:30-12:00 He18, 2.20.
• Thu.,  11.10.2018:  Lecture: 8:45-10:15 He18, 2.20. Lecture: 10:30-12:00 He18, 2.20.
• Fri.,    12.10.2018:  Exercise Class: 8:45-10:15 He18, 1.20.

• Lecture: Monday, 10:00-12:00, He18 - 2.20
• First Lecture: 15/10/2018
• Additional Lecture: 8:30-10:00 19/11/2018
  
• Exercise class: Friday, 08:00-09:00, He18 - E20
• First Exercise class: 19/10/2018
• Tutorial course: Friday, 09:00-10:00, He18 - E20
• First Tutorial course: 19/10/2018
• Additional Exercise Classes/Tutorial Courses: Monday, 08:30-10:00, He18 - 2.20. (12/11/2018 and 10/12/2018)

Final Exam:

written and closed exam of 90 minutes on Monday, 21st January 2019, 10:00-12:00, He18 - 2.20.

Retake of the exam on Thursday, 7th March 2019, 10:00-12:00, He18 - 1.20.

To participate in the written exam, you have to register at campusonline.uni-ulm.de until Wednesday, 16th of January 2019.

Prerequisites:

Analysis I+II and Linear Algebra I.

Contents:

This course covers the basic but nevertheless relevant (especially for Financial Mathematics I) topics of probability theory in a measure-theoretic approach.

Specific topics are

• Definition and properties of measure and the 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