# An Introduction to Measure Theoretic Probability

 Instructor: Dirk Brandes Type: MSc. Finance course News: There is a block course in the last week before the lecture regularly starts, so from 10th of Oct. until 14th of Oct.The schedule is as follow:Mon., 10.10.2016: Lecture: 8:30-12:15 He18, 2.20.Tue., 11.10.2016: Lecture: 8:30-10:00 He18, 2.20; Tutorial: 10:45-12:15  He18, 2.20.Wed., 12.10.2016: Lecture: 8:30-10:00 He18, 2.20; Exercise Class: 10:45-12:15 He18, 2.20.  Thu., 13.10.2016: Lecture: 8:30-12:15 He18, 2.20.  Fri., 14.10.2016: Lecture: 8:30-10:00 He18, 2.20; Exercises Class: 10:45-12:15 He18, 2.20. Time and Venue: Schedule of the course:Lecture: Monday, 10:00-12:00, He18 - 2.20First regular* Lecture: 17/10/2016Last Lecture: 12/12/2016Exercise class: Friday, 13:00-14:00, He18 - E20First regular* Exercise class: 21/10/2016Last Exercise class: 13/01/2017Tutorial course: Friday, 12:00-13:00, He18 - E20First regular* Tutorial course: 21/10/2016Additional Tutorial: 9/01/2017 *after the block course week. Final Exam: written exam on Friday, 20th January 2017, 12:00 - 14:00, He18 - E20, 90 minutes. To participate in the written exam, you have to register at campusonline.uni-ulm.de until Monday, 16th of January 2017. Prerequisites: Analysis I+II and Linear Algebra I. Contents: This course covers the basic facts from probability in a measure-theoretic approach.Specific topics areDefinition 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: Lecture notes: Moodle Additional Material: Refresher in Probability 1Refresher in Probability 2