Lecture Winter Term 2017/2018

An Introduction to Measure Theoretic Probability

 

Lecturer:

Class Teacher:

Imma Curato

Abdulkahar Alkadour


Type:
MSc. Finance course (only)

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.
Time and Venue:Schedule of the course from 16. Oct.  until the christmas
  • 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,  19th of January  2018 and 08th of March 2018., 90 minutes.

To participate in the written exam, you have to register at campusonline.uni-ulm.de.

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:

A list of reference books would cover the following works:
  • 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 

Lecture notes:

Moodle

Additional Material:

Refresher in Probability 1

Refresher in Probability 2